From b832fc3f67231e7f8e7256ef4021ebd94460566a Mon Sep 17 00:00:00 2001 From: tnagler Date: Sun, 23 Aug 2026 22:28:19 +0200 Subject: [PATCH 01/25] Use power transform for one-sided boundaries --- include/kde1d/kde1d.hpp | 62 ++++++++++++++++++++---------- test/test_numerical_invariants.cpp | 16 ++++++++ 2 files changed, 57 insertions(+), 21 deletions(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 22d4920..1f5c750 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -140,8 +140,10 @@ class Kde1d double prob0_{ 0.0 }; double loglik_{ NAN }; double edf_{ NAN }; - // Regularizes one-sided log transforms in the units of the fitted data. + // Regularizes one-sided power transforms in the units of the fitted data. double boundary_offset_{ NAN }; + // Makes one-sided transforms dimensionless and scale equivariant. + double boundary_scale_{ 1.0 }; static constexpr double K0_ = 0.3989425; // private methods @@ -363,16 +365,16 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) else distances = xx.array() - xmin_; if (w.size() == 0) { - boundary_offset_ = 1e-5 * stats::median(distances); + boundary_scale_ = stats::median(distances); } else { - boundary_offset_ = - 1e-5 * stats::quantile( - distances, Eigen::VectorXd::Constant(1, 0.5), w)(0); + boundary_scale_ = stats::quantile( + distances, Eigen::VectorXd::Constant(1, 0.5), w)(0); } - if (!(boundary_offset_ > 0.0)) - boundary_offset_ = 1e-5 * distances.maxCoeff(); - if (!(boundary_offset_ > 0.0)) - boundary_offset_ = 1e-5; + if (!(boundary_scale_ > 0.0)) + boundary_scale_ = distances.maxCoeff(); + if (!(boundary_scale_ > 0.0)) + boundary_scale_ = 1.0; + boundary_offset_ = 1e-5 * boundary_scale_; } xx = boundary_transform(xx); @@ -779,11 +781,17 @@ Kde1d::boundary_transform(const Eigen::VectorXd& x, bool inverse) x_new = (x.array() - xmin_ + 5e-5 * rng) / (1.0001 * rng); x_new = stats::qnorm(x_new); } else if (!std::isnan(xmin_)) { - // left boundary -> log transform - x_new = (boundary_offset_ + x.array() - xmin_).log(); + // left boundary -> power-3/4 transform + x_new = 4.0 * (((boundary_offset_ + x.array() - xmin_) / + boundary_scale_) + .pow(0.25) - + std::pow(boundary_offset_ / boundary_scale_, 0.25)); } else if (!std::isnan(xmax_)) { - // right boundary -> negative log transform - x_new = (boundary_offset_ + xmax_ - x.array()).log(); + // right boundary -> reflected power-3/4 transform + x_new = 4.0 * (((boundary_offset_ + xmax_ - x.array()) / + boundary_scale_) + .pow(0.25) - + std::pow(boundary_offset_ / boundary_scale_, 0.25)); } else { // no boundary -> no transform } @@ -793,11 +801,19 @@ Kde1d::boundary_transform(const Eigen::VectorXd& x, bool inverse) auto rng = xmax_ - xmin_; x_new = stats::pnorm(x).array() * 1.0001 * rng + xmin_ - 5e-5 * rng; } else if (!std::isnan(xmin_)) { - // left boundary -> log transform - x_new = x.array().exp() + xmin_ - boundary_offset_; + // left boundary -> inverse power-3/4 transform + x_new = boundary_scale_ * + (x.array() / 4.0 + + std::pow(boundary_offset_ / boundary_scale_, 0.25)) + .pow(4) + + xmin_ - boundary_offset_; } else if (!std::isnan(xmax_)) { - // right boundary -> negative log transform - x_new = -(x.array().exp() - xmax_ - boundary_offset_); + // right boundary -> inverse reflected power-3/4 transform + x_new = xmax_ + boundary_offset_ - + boundary_scale_ * + (x.array() / 4.0 + + std::pow(boundary_offset_ / boundary_scale_, 0.25)) + .pow(4); } else { // no boundary -> no transform } @@ -827,11 +843,15 @@ Kde1d::boundary_correct(const Eigen::VectorXd& x, const Eigen::VectorXd& fhat) corr_term /= (xmax_ - xmin_ + 1e-4 * rng); corr_term = 1.0 / corr_term.array(); } else if (!std::isnan(xmin_)) { - // left boundary -> log transform - corr_term = 1.0 / (boundary_offset_ + x.array() - xmin_); + // left boundary -> power-3/4 transform + corr_term = ((boundary_offset_ + x.array() - xmin_) / boundary_scale_) + .pow(-0.75) / + boundary_scale_; } else if (!std::isnan(xmax_)) { - // right boundary -> negative log transform - corr_term = 1.0 / (boundary_offset_ + xmax_ - x.array()); + // right boundary -> reflected power-3/4 transform + corr_term = ((boundary_offset_ + xmax_ - x.array()) / boundary_scale_) + .pow(-0.75) / + boundary_scale_; } else { // no boundary -> no transform corr_term.fill(1.0); diff --git a/test/test_numerical_invariants.cpp b/test/test_numerical_invariants.cpp index c726e9d..98e8c86 100644 --- a/test/test_numerical_invariants.cpp +++ b/test/test_numerical_invariants.cpp @@ -128,6 +128,22 @@ TEST_CASE("one-sided fits are scale equivariant", } } +TEST_CASE("one-sided power grids do not explode on exponential data", + "[numerical-invariants][boundary-grid]") +{ + Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(500, 0.5 / 500.0, 1.0 - 0.5 / 500.0); + Eigen::VectorXd observations = (-(1.0 - probabilities.array()).log()); + kde1d::Kde1d fit(0.0, NAN, "continuous"); + fit.fit(observations); + + Eigen::VectorXd boundary_density = + fit.pdf(Eigen::VectorXd::Constant(1, 0.0)); + CHECK(fit.get_grid_points().maxCoeff() < 10.0 * observations.maxCoeff()); + CHECK(std::isfinite(boundary_density(0))); + CHECK(boundary_density(0) > 0.0); +} + TEST_CASE("interpolation preserves nonuniform-grid reference values", "[interpolation][parity]") { From ff52268ea87e3f37cc159cbb5a893b91ab51651d Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 13:15:26 +0200 Subject: [PATCH 02/25] Add two-sided boundary repair reference --- diagnostic/README.md | 4 + diagnostic/boundary-repair/HANDOFF.md | 50 +++ diagnostic/boundary-repair/NATIVE_CPP.md | 88 ++++ diagnostic/boundary-repair/README.md | 67 ++++ diagnostic/boundary-repair/RESULTS.md | 59 +++ .../plots/bounded-estimator-validation.pdf | Bin 0 -> 70646 bytes .../plots/endpoint-classifier-ablation.pdf | Bin 0 -> 77147 bytes .../results/bounded-estimator-validation.csv | 25 ++ .../results/endpoint-classifier-ablation.csv | 85 ++++ .../scripts/ablate_endpoint_classifier.R | 235 +++++++++++ .../scripts/bounded_estimator.R | 376 ++++++++++++++++++ .../plot_bounded_estimator_validation.R | 208 ++++++++++ .../plot_endpoint_classifier_ablation.R | 234 +++++++++++ .../scripts/validate_bounded_estimator.R | 195 +++++++++ 14 files changed, 1626 insertions(+) create mode 100644 diagnostic/boundary-repair/HANDOFF.md create mode 100644 diagnostic/boundary-repair/NATIVE_CPP.md create mode 100644 diagnostic/boundary-repair/README.md create mode 100644 diagnostic/boundary-repair/RESULTS.md create mode 100644 diagnostic/boundary-repair/plots/bounded-estimator-validation.pdf create mode 100644 diagnostic/boundary-repair/plots/endpoint-classifier-ablation.pdf create mode 100644 diagnostic/boundary-repair/results/bounded-estimator-validation.csv create mode 100644 diagnostic/boundary-repair/results/endpoint-classifier-ablation.csv create mode 100644 diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R create mode 100644 diagnostic/boundary-repair/scripts/bounded_estimator.R create mode 100644 diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R create mode 100644 diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R create mode 100644 diagnostic/boundary-repair/scripts/validate_bounded_estimator.R diff --git a/diagnostic/README.md b/diagnostic/README.md index d34d715..7466023 100644 --- a/diagnostic/README.md +++ b/diagnostic/README.md @@ -29,3 +29,7 @@ where the true density vanishes, while CDF error can remain small despite a severely unstable pointwise density. Candidate repairs should therefore be checked against both finite nonzero boundary densities and densities that tend to zero. + +The separate transformation-boundary investigation, its retained simulation +results, and its current recommendations live in +[`boundary-repair/`](boundary-repair/README.md). diff --git a/diagnostic/boundary-repair/HANDOFF.md b/diagnostic/boundary-repair/HANDOFF.md new file mode 100644 index 0000000..92a57ed --- /dev/null +++ b/diagnostic/boundary-repair/HANDOFF.md @@ -0,0 +1,50 @@ +# Two-boundary repair handoff + +## Current state + +The directory now contains one experimental estimator for continuous data +with two known finite bounds. It fits the current probit bulk estimator once, +adds an equal local-linear/local-quadratic expert for confidently finite +endpoints, and otherwise reuses bulk. Smooth CDF-scale gates shrink as +$n^{-1/2}$. The finite-endpoint classifier uses +$k=\min(n-1,\lceil2\sqrt n\rceil)$ order statistics and a 95% decision. + +There is no exploding-tail expert, power warp, transformation offset, or CV +selector. Superseded oversmoothing and offset code and outputs were removed. +The retained 100-replication validation and classifier ablation are summarized +in `RESULTS.md`. + +## Reproduce + +From the R-package root: + +```sh +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R 100 +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R +``` + +For a smoke test, pass a smaller replication count and temporary output path +as the first two arguments to either simulation script. + +## Known limitations + +- The R reference assumes support $[0,1]$; native code must apply an affine + map for arbitrary finite bounds. +- Weighted observations have not been specified or validated for the tail + index, weighted ranks, or shrinking gate. +- The finite-versus-bulk decision is hard, so between-sample endpoint behavior + can still change discretely. +- Before release, test affine support changes, weaker and stronger endpoint + singularities, interior modes, ties, and weighted data. + +## Next work + +The immediate next investigation is the analogous one-sided estimator. Keep +that work in a separate sibling diagnostic directory so this two-boundary +reference remains stable. Native implementation of this estimator should +follow `NATIVE_CPP.md` after the one-sided design has settled enough to assess +shared infrastructure. + +Unrelated top-level generated documentation changes were left untouched. diff --git a/diagnostic/boundary-repair/NATIVE_CPP.md b/diagnostic/boundary-repair/NATIVE_CPP.md new file mode 100644 index 0000000..1672e4a --- /dev/null +++ b/diagnostic/boundary-repair/NATIVE_CPP.md @@ -0,0 +1,88 @@ +# Native C++ implementation plan + +## Integration point + +The production estimator belongs in +`include/kde1d/kde1d.hpp`, where `Kde1d::fit()` currently handles bounded +continuous data through a single probit-transformed local-likelihood fit. The +new path should activate only when both bounds are finite and the variable is +continuous. One-sided, unbounded, discrete, and zero-inflated behavior should +remain unchanged. + +Avoid implementing the method through recursively constructed public +`Kde1d` objects: a nested bounded fit would activate the boundary selector +again. Extract the existing bounded-probit calculation into a private helper, +or introduce an internal mode that requests the legacy transformation fit +directly. + +## Components to implement + +1. Normalize observations and grid locations to $[0,1]$ using the supplied + finite support. Convert final density values back with the inverse support + length. This must preserve affine equivariance. +2. Fit the unweighted legacy probit bulk estimator once. Retain its PDF, CDF, + and final original-scale grid. +3. Compute $k=\min(n-1,\lceil2\sqrt n\rceil)$ and the two order-statistic tail + indices. Use a partial selection algorithm if convenient, although a full + sort is acceptable initially. Protect zero endpoint distances with the C++ + equivalent of `std::numeric_limits::epsilon()`. +4. Classify each endpoint as finite or bulk using the fixed finite-endpoint + rule in `README.md`. Exploding, vanishing, and ambiguous cases all use bulk. +5. Construct rank-based lower and upper bandwidth weights using average ranks + for ties and boundary fraction $\min(0.25,n^{-1/2})$. +6. Add a private Gaussian equivalent-kernel evaluator for boundary polynomial + degrees one and two. Select each bandwidth through + `bandwidth::PluginBandwidthSelector` with endpoint weights, impose the + corresponding full-sample unweighted bandwidth as its floor, but evaluate + density contributions with equal observation weights. Reflect data and + grid locations for the upper endpoint. +7. Average the degree-one and degree-two endpoint densities. Clamp negative + component values to zero before component normalization, matching the R + reference. +8. Obtain fusion probabilities from the bulk CDF and evaluate the smoothstep + gates. Substitute bulk or finite component values according to each + endpoint decision, fuse arithmetically, clamp at zero, and normalize on the + final grid. +9. Store the fused values in `interp::InterpolationGrid` so existing PDF, + CDF, quantile, and simulation methods continue to work without a new + public fitted-object representation. + +## API and metadata decisions + +The first implementation can keep the method automatic for two finite bounds, +but an internal feature switch is useful while validating. Decide whether the +selector threshold and gate constants remain private or become advanced API +parameters; the current recommendation is to keep them fixed until broader +validation justifies exposing them. + +`loglik_` can be recomputed from the final interpolated density. Effective +degrees of freedom do not combine trivially across selected and fused experts; +do not silently reuse the bulk value. Either derive the fused influence trace +or return `NaN` for `edf_` until a principled definition is implemented. + +The public API accepts case weights, while the retained experiment is +unweighted. Before enabling the new estimator for weighted fits, define: + +- weighted ranks and tie handling for endpoint bandwidth weights; +- an effective sample size for $k$ and the shrinking gate; +- a weighted order-statistic tail index; +- whether selector confidence adjustments use raw or effective sample size. + +Until those choices are validated, weighted bounded fits should remain on the +legacy path rather than pretending the unweighted selector applies. + +## Tests required + +- Golden PDF vectors against `scripts/bounded_estimator.R` for fixed Uniform, + Beta$(1,2)$, Beta$(0.75,2)$, and Beta$(0.75,0.75)$ samples. +- Explicit samples that select bulk and finite behavior at each endpoint, + including asymmetric lower/upper decisions. +- Nonnegativity, unit mass, monotone CDF, inverse-CDF consistency, and support + truncation. +- Affine-equivariance tests on intervals such as $[-3,7]$. +- Stability with ties, observations exactly at a bound, small samples, and + nearly degenerate samples. +- Regression tests proving that one-sided, unbounded, discrete, + zero-inflated, and weighted fits retain their existing behavior. +- A native rerun of the retained 100-replication validation before making the + new path the default. diff --git a/diagnostic/boundary-repair/README.md b/diagnostic/boundary-repair/README.md new file mode 100644 index 0000000..fb263e1 --- /dev/null +++ b/diagnostic/boundary-repair/README.md @@ -0,0 +1,67 @@ +# Two-sided boundary repair + +This directory contains the selected experimental estimator for continuous +densities on a known finite interval, its paired validation against the +current probit estimator, and the retained endpoint-classifier ablation. + +## Selected estimator + +The reference implementation assumes the support has been mapped affinely to +$[0,1]$. First fit the current unweighted probit estimator $\widehat f_B$ and +use its CDF to define sample-shrinking endpoint gates. With +$r_n=\min(0.25,n^{-1/2})$ and $s(t)=3t^2-2t^3$, + +$$ +w_L(x)=1-s\left(\min\left\{1,\frac{\widehat F_B(x)}{r_n}\right\}\right), +\qquad +w_U(x)=1-s\left(\min\left\{1,\frac{1-\widehat F_B(x)}{r_n}\right\}\right), +$$ + +and $w_B(x)=1-w_L(x)-w_U(x)$. The finite-boundary expert is the +equal average of Gaussian equivalent-kernel local-linear and local-quadratic +estimates. Rank-based endpoint weights select their bandwidths, but density +contributions remain unweighted, so the estimand does not change. Negative +component values are truncated during normalization. + +Finite endpoint behavior is identified from +$k=\min(n-1,\lceil2\sqrt n\rceil)$ order statistics. At the lower endpoint, + +$$ +\widehat\beta_L += +\frac{k}{\sum_{i=1}^k +\log\{X_{(k+1)}/X_{(i)}\}}, +$$ + +with the analogous calculation on $1-X$ at the upper endpoint. The finite +expert is used if +$\widehat\beta\geq0.9$ and +$\widehat\beta(1-1.645/\sqrt{k})\leq1$; otherwise the endpoint reuses the bulk +estimator. Thus exploding, vanishing, and ambiguous endpoints require no +additional fit. + +The finite or bulk endpoint components are fused with $w_L,w_B,w_U$, +truncated at zero, and normalized numerically. There is no power transform, +offset transform, oversmoothed tail expert, or cross-validation selector. + +## Retained files + +- `scripts/bounded_estimator.R`: self-contained R reference implementation. +- `scripts/validate_bounded_estimator.R`: paired validation against current. +- `scripts/plot_bounded_estimator_validation.R`: numerical and realization + report. +- `scripts/ablate_endpoint_classifier.R`: paired classifier ablation. +- `scripts/plot_endpoint_classifier_ablation.R`: classifier report. +- `results/` and `plots/`: corresponding 100-replication outputs. +- `RESULTS.md`: final numerical conclusions. +- `HANDOFF.md`: concise continuation state. +- `NATIVE_CPP.md`: native C++ implementation plan. + +Run from the R-package root: + +```sh +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R 100 +Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R +``` diff --git a/diagnostic/boundary-repair/RESULTS.md b/diagnostic/boundary-repair/RESULTS.md new file mode 100644 index 0000000..128f69e --- /dev/null +++ b/diagnostic/boundary-repair/RESULTS.md @@ -0,0 +1,59 @@ +# Validation results + +## Final estimator + +The final two-boundary estimator combines the current probit bulk fit with an +equal local-linear/local-quadratic expert at endpoints classified as finite. +All other endpoint types reuse bulk. The validation uses 100 paired +replications for Uniform, Beta$(1,2)$, Beta$(0.75,2)$, and +Beta$(0.75,0.75)$ at $n=100,1000,2000$. The primary measure is integrated +squared error (ISE). + +Global ISE ratios to the current bounded estimator are: + +| density | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:| +| Uniform | 0.884 | 0.830 | 0.814 | +| Beta$(1,2)$ | 0.879 | 0.818 | 0.802 | +| Beta$(0.75,2)$ | 0.943 | 1.050 | 1.045 | +| Beta$(0.75,0.75)$ | 0.945 | 1.037 | 1.033 | + +Mean ratios across the four densities are 0.913, 0.934, and 0.923. The +finite-endpoint cases improve clearly. Losses for exploding densities are +small and accepted in exchange for keeping a generic, shape-agnostic finite +expert. + +All retained estimates are nonnegative and normalized numerically. The +maximum mass error in the validation is $2.2\times10^{-16}$. + +## Endpoint classifier + +The selected rule uses one tail-index estimate with +$k=\min(n-1,\lceil2\sqrt n\rceil)$ and a 95% finite-endpoint decision. It was +compared with single scales $\sqrt n$ and $1.5\sqrt n$, and multiscale median +and voting rules. Mean ISE ratios to current are: + +| $n$ | $\sqrt n$, 95% | $2\sqrt n$, 95% | multiscale vote, 90% | +|---:|---:|---:|---:| +| 100 | 0.885 | 0.912 | 0.919 | +| 1000 | 0.976 | 0.936 | 0.996 | +| 2000 | 0.994 | 0.921 | 0.981 | + +The smaller scale is slightly better at $n=100$, but $2\sqrt n$ is clearly +better at $n=1000,2000$ and substantially reduces the worst exploding-tail +loss. Multiscale classification adds complexity without improving ISE or the +representative fits. + +## Bulk decision for nonfinite endpoints + +A final focused comparison used asymmetric Beta$(a,2)$ and symmetric +Beta$(a,a)$ densities for $a=0.9,0.75,0.6$. An oversmoothed probit tail reduced +integrated variance by roughly one third, but its mean ISE ratios to simply +reusing bulk were 0.948, 1.079, and 1.095 at $n=100,1000,2000$. Bulk won all +six large-sample scenarios. The additional transformed fit, offset, bandwidth +multiplier, and fusion branch were therefore removed from the selected +estimator. + +The retained CSVs contain global and endpoint-local ISE, squared bias, +integrated variance, selection rates, minimum density, and mass error. 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!file.exists("DESCRIPTION")) { + stop("run from the kde1d package root with pkgload installed") +} +pkgload::load_all(".", quiet = TRUE) +source(paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", + "bounded_estimator.R" +)) + +arguments <- commandArgs(trailingOnly = TRUE) +replication_count <- if (length(arguments) >= 1L) { + as.integer(arguments[[1L]]) +} else { + 100L +} +output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", + "endpoint-classifier-ablation.csv" +) +if (length(arguments) > 2L || !is.finite(replication_count) || + replication_count < 2L) { + stop("usage: ablate_endpoint_classifier.R [replications] [output.csv]") +} + +make_beta_distribution <- function(shape1, shape2, endpoint_truth) { + list( + random = function(sample_size) rbeta(sample_size, shape1, shape2), + density = function(values) dbeta(values, shape1, shape2), + endpoint_truth = endpoint_truth + ) +} +validation_distributions <- list( + uniform = list( + random = runif, + density = dunif, + endpoint_truth = c(lower = "finite", upper = "finite") + ), + `beta-1-2` = make_beta_distribution( + 1, 2, c(lower = "finite", upper = "bulk") + ), + `beta-0.75-2` = make_beta_distribution( + 0.75, 2, c(lower = "bulk", upper = "bulk") + ), + `beta-0.75-0.75` = make_beta_distribution( + 0.75, 0.75, c(lower = "bulk", upper = "bulk") + ) +) +sample_sizes <- c(100L, 1000L, 2000L) +classifier_methods <- c( + "single-95", "single-1.5-95", "single-2-95", + "median-90", "vote-90", "vote-95" +) +methods <- c("kde-current", classifier_methods) +evaluation_points <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.99, length.out = 301L), + 1 - 10^seq(-2, -10, length.out = 101L) +))) +left_points <- evaluation_points <= 0.1 +right_points <- evaluation_points >= 0.9 +result_rows <- list() + +make_classifier_selections <- function(observations) { + list( + `single-95` = select_bounded_endpoint_experts_single_scale(observations), + `single-1.5-95` = select_bounded_endpoint_experts_single_scale( + observations, + tail_multiplier = 1.5 + ), + `single-2-95` = select_bounded_endpoint_experts_single_scale( + observations, + tail_multiplier = 2 + ), + `median-90` = select_bounded_endpoint_experts_multiscale( + observations, + evidence_threshold = qnorm(0.90), + rule = "median" + ), + `vote-90` = select_bounded_endpoint_experts_multiscale( + observations, + evidence_threshold = qnorm(0.90), + rule = "vote" + ), + `vote-95` = select_bounded_endpoint_experts_multiscale( + observations, + evidence_threshold = qnorm(0.95), + rule = "vote" + ) + ) +} + +summarize_estimates <- function(estimates, true_density, region_points) { + mean_density <- rowMeans(estimates) + integrated_errors <- vapply( + seq_len(ncol(estimates)), + function(replication) { + trapezoid_integral( + evaluation_points[region_points], + (estimates[region_points, replication] - + true_density[region_points])^2 + ) + }, + numeric(1L) + ) + c( + ise = mean(integrated_errors), + squared_bias = trapezoid_integral( + evaluation_points[region_points], + (mean_density[region_points] - true_density[region_points])^2 + ), + variance = trapezoid_integral( + evaluation_points[region_points], + rowMeans((estimates[region_points, , drop = FALSE] - + mean_density[region_points])^2) + ) + ) +} + +for (distribution_index in seq_along(validation_distributions)) { + true_density <- validation_distributions[[distribution_index]]$density( + evaluation_points + ) + for (sample_size in sample_sizes) { + estimates <- setNames( + lapply(methods, function(method) { + matrix(NA_real_, length(evaluation_points), replication_count) + }), + methods + ) + choices <- setNames( + lapply(classifier_methods, function(method) { + matrix( + NA_character_, replication_count, 2L, + dimnames = list(NULL, c("lower", "upper")) + ) + }), + classifier_methods + ) + for (replication in seq_len(replication_count)) { + set.seed( + 20260909L + 100000L * distribution_index + + 1000L * match(sample_size, sample_sizes) + replication + ) + observations <- validation_distributions[[distribution_index]]$random( + sample_size + ) + estimates$`kde-current`[, replication] <- normalize_density( + evaluation_points, + dkde1d( + evaluation_points, + kde1d(observations, xmin = 0, xmax = 1) + ) + ) + estimator_components <- fit_bounded_estimator_components( + observations, + evaluation_points + ) + classifier_selections <- make_classifier_selections(observations) + for (method in classifier_methods) { + estimator_components$selection <- classifier_selections[[method]] + estimates[[method]][, replication] <- + fuse_bounded_estimator_components( + evaluation_points, + estimator_components + )$density + choices[[method]][replication, ] <- + classifier_selections[[method]]$expert_choices + } + } + for (method in methods) { + global_summary <- summarize_estimates( + estimates[[method]], true_density, rep(TRUE, length(evaluation_points)) + ) + left_summary <- summarize_estimates( + estimates[[method]], true_density, left_points + ) + right_summary <- summarize_estimates( + estimates[[method]], true_density, right_points + ) + endpoint_truth <- validation_distributions[[distribution_index]]$endpoint_truth + result_rows[[length(result_rows) + 1L]] <- data.frame( + distribution = names(validation_distributions)[[distribution_index]], + sample_size = sample_size, + replications = replication_count, + method = method, + global_ise = global_summary[["ise"]], + global_squared_bias = global_summary[["squared_bias"]], + global_variance = global_summary[["variance"]], + left_ise = left_summary[["ise"]], + left_squared_bias = left_summary[["squared_bias"]], + left_variance = left_summary[["variance"]], + right_ise = right_summary[["ise"]], + right_squared_bias = right_summary[["squared_bias"]], + right_variance = right_summary[["variance"]], + lower_accuracy = if (method == "kde-current") { + NA_real_ + } else { + mean(choices[[method]][, "lower"] == endpoint_truth[["lower"]]) + }, + upper_accuracy = if (method == "kde-current") { + NA_real_ + } else { + mean(choices[[method]][, "upper"] == endpoint_truth[["upper"]]) + }, + lower_finite_rate = if (method == "kde-current") NA_real_ else + mean(choices[[method]][, "lower"] == "finite"), + upper_finite_rate = if (method == "kde-current") NA_real_ else + mean(choices[[method]][, "upper"] == "finite"), + minimum_density = min(estimates[[method]]), + maximum_mass_error = max(abs(vapply( + seq_len(replication_count), + function(replication) { + trapezoid_integral( + evaluation_points, + estimates[[method]][, replication] + ) - 1 + }, + numeric(1L) + ))) + ) + } + message( + names(validation_distributions)[[distribution_index]], + ", n = ", sample_size + ) + } +} + +results <- do.call(rbind, result_rows) +dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) +write.csv(results, output_file, row.names = FALSE) +message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary-repair/scripts/bounded_estimator.R b/diagnostic/boundary-repair/scripts/bounded_estimator.R new file mode 100644 index 0000000..7ef12c0 --- /dev/null +++ b/diagnostic/boundary-repair/scripts/bounded_estimator.R @@ -0,0 +1,376 @@ +# Reference R implementation of the selected two-sided boundary estimator. + +trapezoid_integral <- function(evaluation_points, values) { + sum(diff(evaluation_points) * + (values[-length(values)] + values[-1L]) / 2) +} + +normalize_density <- function(evaluation_points, density) { + density <- pmax(0, density) + density_mass <- trapezoid_integral(evaluation_points, density) + if (!is.finite(density_mass) || density_mass <= 0) { + stop("density cannot be normalized") + } + density / density_mass +} + +smoothstep <- function(normalized_distance) { + 3 * normalized_distance^2 - 2 * normalized_distance^3 +} + +make_bounded_expert_weights <- function(probabilities, sample_size, + concentration = 1, + shrinkage_exponent = 0.5) { + boundary_fraction <- min( + 0.25, + concentration / sample_size^shrinkage_exponent + ) + lower_weights <- 1 - smoothstep(pmin(1, probabilities / boundary_fraction)) + upper_weights <- 1 - smoothstep(pmin( + 1, + (1 - probabilities) / boundary_fraction + )) + cbind( + lower = lower_weights, + bulk = pmax(0, 1 - lower_weights - upper_weights), + upper = upper_weights + ) +} + +fit_local_polynomial_boundary <- function( + observations, + evaluation_points, + bandwidth_weights, + minimum_bandwidth, + degree) { + if (!degree %in% c(1, 2)) { + stop("local boundary degree must be 1 or 2") + } + selected_bandwidth <- kde1d( + observations, + weights = bandwidth_weights, + deg = degree + )$bw + bandwidth <- max(selected_bandwidth, minimum_bandwidth) + standardized_boundary <- evaluation_points / bandwidth + truncated_moment_0 <- pnorm(standardized_boundary) + truncated_moment_1 <- -dnorm(standardized_boundary) + truncated_moment_2 <- truncated_moment_0 - + standardized_boundary * dnorm(standardized_boundary) + if (degree == 1) { + moment_determinant <- truncated_moment_0 * truncated_moment_2 - + truncated_moment_1^2 + equivalent_kernel_coefficients <- cbind( + truncated_moment_2 / moment_determinant, + -truncated_moment_1 / moment_determinant + ) + } else { + truncated_moment_3 <- -( + standardized_boundary^2 + 2 + ) * dnorm(standardized_boundary) + truncated_moment_4 <- 3 * truncated_moment_0 - ( + standardized_boundary^3 + 3 * standardized_boundary + ) * dnorm(standardized_boundary) + moment_determinant <- + truncated_moment_0 * ( + truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 + ) - + truncated_moment_1 * ( + truncated_moment_1 * truncated_moment_4 - + truncated_moment_2 * truncated_moment_3 + ) + + truncated_moment_2 * ( + truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 + ) + equivalent_kernel_coefficients <- cbind( + ( + truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 + ) / moment_determinant, + ( + truncated_moment_2 * truncated_moment_3 - + truncated_moment_1 * truncated_moment_4 + ) / moment_determinant, + ( + truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 + ) / moment_determinant + ) + } + density <- numeric(length(evaluation_points)) + for (chunk_start in seq(1L, length(evaluation_points), by = 128L)) { + chunk_indices <- chunk_start:min( + chunk_start + 127L, + length(evaluation_points) + ) + kernel_arguments <- outer( + evaluation_points[chunk_indices], + observations, + "-" + ) / bandwidth + base_kernels <- dnorm(kernel_arguments) + corrected_kernels <- base_kernels * + equivalent_kernel_coefficients[chunk_indices, 1L] + for (polynomial_order in seq_len(degree)) { + corrected_kernels <- corrected_kernels + + base_kernels * + equivalent_kernel_coefficients[ + chunk_indices, + polynomial_order + 1L + ] * kernel_arguments^polynomial_order + } + density[chunk_indices] <- rowMeans(corrected_kernels) / bandwidth + } + list( + density = normalize_density(evaluation_points, density), + bandwidth = bandwidth, + selected_bandwidth = selected_bandwidth + ) +} + +fit_bounded_finite_expert <- function(observations, evaluation_points, + concentration = 1, + shrinkage_exponent = 0.5) { + probability_ranks <- (rank(observations, ties.method = "average") - 0.5) / + length(observations) + bandwidth_weights <- make_bounded_expert_weights( + probability_ranks, + length(observations), + concentration, + shrinkage_exponent + ) + bulk_model <- kde1d(observations, xmin = 0, xmax = 1) + bulk_density <- normalize_density( + evaluation_points, + dkde1d(evaluation_points, bulk_model) + ) + endpoint_densities <- lapply(c(1L, 2L), function(degree) { + minimum_bandwidth <- kde1d(observations, deg = degree)$bw + lower_density <- fit_local_polynomial_boundary( + observations, + evaluation_points, + bandwidth_weights[, "lower"], + minimum_bandwidth, + degree + )$density + upper_density <- rev(fit_local_polynomial_boundary( + 1 - observations, + rev(1 - evaluation_points), + bandwidth_weights[, "upper"], + minimum_bandwidth, + degree + )$density) + cbind(lower = lower_density, bulk = bulk_density, upper = upper_density) + }) + component_densities <- ( + endpoint_densities[[1L]] + endpoint_densities[[2L]] + ) / 2 + evaluation_weights <- make_bounded_expert_weights( + pkde1d(evaluation_points, bulk_model), + length(observations), + concentration, + shrinkage_exponent + ) + list( + density = normalize_density( + evaluation_points, + rowSums(evaluation_weights * component_densities) + ), + component_densities = component_densities, + evaluation_weights = evaluation_weights, + boundary_fraction = min( + 0.25, + concentration / length(observations)^shrinkage_exponent + ) + ) +} + +estimate_bounded_tail_indices <- function(observations, tail_counts) { + if (any(tail_counts < 1L) || any(tail_counts >= length(observations))) { + stop("tail_counts must be between one and sample size minus one") + } + ordered_observations <- sort(observations) + upper_distances <- sort(1 - observations) + tail_indices <- vapply(tail_counts, function(tail_count) { + c( + lower = tail_count / sum(log( + ordered_observations[[tail_count + 1L]] / + pmax( + .Machine$double.eps, + ordered_observations[seq_len(tail_count)] + ) + )), + upper = tail_count / sum(log( + upper_distances[[tail_count + 1L]] / + pmax(.Machine$double.eps, upper_distances[seq_len(tail_count)]) + )) + ) + }, numeric(2L)) + if (length(tail_counts) == 1L) { + tail_indices <- matrix( + tail_indices, + nrow = 2L, + dimnames = list(c("lower", "upper"), NULL) + ) + } + rownames(tail_indices) <- c("lower", "upper") + colnames(tail_indices) <- as.character(tail_counts) + tail_indices +} + +select_bounded_endpoint_experts_single_scale <- function( + observations, + tail_multiplier = 1, + evidence_threshold = qnorm(0.95), + minimum_finite_index = 0.9) { + if (!is.finite(tail_multiplier) || tail_multiplier <= 0) { + stop("tail_multiplier must be finite and positive") + } + tail_count <- min( + length(observations) - 1L, + ceiling(tail_multiplier * sqrt(length(observations))) + ) + tail_indices <- estimate_bounded_tail_indices( + observations, + tail_count + )[, 1L] + expert_choices <- rep("bulk", length(tail_indices)) + names(expert_choices) <- names(tail_indices) + expert_choices[ + tail_indices >= minimum_finite_index & + tail_indices * (1 - evidence_threshold / sqrt(tail_count)) <= 1 + ] <- "finite" + list( + expert_choices = expert_choices, + tail_indices = tail_indices, + tail_count = tail_count, + evidence_threshold = evidence_threshold, + minimum_finite_index = minimum_finite_index + ) +} + +select_bounded_endpoint_experts_multiscale <- function( + observations, + evidence_threshold = qnorm(0.90), + tail_multipliers = c(1, 1.5, 2), + maximum_tail_fraction = 0.15, + rule = c("vote", "median")) { + rule <- match.arg(rule) + tail_counts <- pmin( + floor(maximum_tail_fraction * length(observations)), + ceiling(tail_multipliers * sqrt(length(observations))) + ) + tail_counts <- pmax(1L, pmin(length(observations) - 1L, tail_counts)) + tail_indices <- estimate_bounded_tail_indices(observations, tail_counts) + standardized_indices <- sweep( + log(tail_indices), + 2L, + sqrt(tail_counts), + "*" + ) + expert_choices <- apply(standardized_indices, 1L, function(scores) { + if (rule == "median") { + median_score <- median(scores) + if (abs(median_score) <= evidence_threshold) { + "finite" + } else { + "bulk" + } + } else { + required_votes <- floor(length(scores) / 2) + 1L + if (sum(abs(scores) <= evidence_threshold) >= required_votes) { + "finite" + } else { + "bulk" + } + } + }) + list( + expert_choices = expert_choices, + tail_indices = tail_indices, + standardized_indices = standardized_indices, + tail_counts = tail_counts, + evidence_threshold = evidence_threshold, + tail_multipliers = tail_multipliers, + maximum_tail_fraction = maximum_tail_fraction, + rule = rule + ) +} + +select_bounded_endpoint_experts <- function( + observations, + evidence_threshold = qnorm(0.95), + minimum_finite_index = 0.9) { + select_bounded_endpoint_experts_single_scale( + observations, + tail_multiplier = 2, + evidence_threshold, + minimum_finite_index + ) +} + +fit_bounded_estimator_components <- function( + observations, + evaluation_points, + concentration = 1, + shrinkage_exponent = 0.5) { + if (length(observations) < 4L || any(!is.finite(observations)) || + any(observations < 0 | observations > 1)) { + stop("observations must contain at least four finite values in [0, 1]") + } + if (any(!is.finite(evaluation_points)) || + is.unsorted(evaluation_points, strictly = TRUE) || + any(evaluation_points < 0 | evaluation_points > 1)) { + stop("evaluation_points must be strictly increasing in [0, 1]") + } + finite_fit <- fit_bounded_finite_expert( + observations, + evaluation_points, + concentration, + shrinkage_exponent + ) + selection <- select_bounded_endpoint_experts(observations) + list( + finite_fit = finite_fit, + selection = selection + ) +} + +fuse_bounded_estimator_components <- function( + evaluation_points, + estimator_components) { + finite_fit <- estimator_components$finite_fit + selection <- estimator_components$selection + component_densities <- finite_fit$component_densities + for (boundary in c("lower", "upper")) { + if (selection$expert_choices[[boundary]] != "finite") { + component_densities[, boundary] <- component_densities[, "bulk"] + } + } + list( + density = normalize_density( + evaluation_points, + rowSums(finite_fit$evaluation_weights * component_densities) + ), + component_densities = component_densities, + evaluation_weights = finite_fit$evaluation_weights, + expert_choices = selection$expert_choices, + tail_indices = selection$tail_indices, + tail_count = selection$tail_count, + boundary_fraction = finite_fit$boundary_fraction + ) +} + +fit_bounded_selected_estimator <- function( + observations, + evaluation_points, + concentration = 1, + shrinkage_exponent = 0.5) { + fuse_bounded_estimator_components( + evaluation_points, + fit_bounded_estimator_components( + observations, + evaluation_points, + concentration, + shrinkage_exponent + ) + ) +} diff --git a/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R b/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R new file mode 100644 index 0000000..ddb2597 --- /dev/null +++ b/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R @@ -0,0 +1,208 @@ +# Plot the paired validation of the selected bounded estimator. +# Run from the root of the kde1d R package. + +if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { + stop("run from the kde1d package root with pkgload installed") +} +pkgload::load_all(".", quiet = TRUE) +source(paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", + "bounded_estimator.R" +)) + +arguments <- commandArgs(trailingOnly = TRUE) +input_file <- if (length(arguments) >= 1L) arguments[[1L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", + "bounded-estimator-validation.csv" +) +output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/plots/", + "bounded-estimator-validation.pdf" +) +if (length(arguments) > 2L) { + stop("usage: plot_bounded_estimator_validation.R [input.csv] [output.pdf]") +} + +results <- read.csv(input_file) +replication_count <- unique(results$replications) +if (length(replication_count) != 1L) { + stop("input must contain a single replication count") +} +method_colors <- c(current = "grey45", selected = "#009E73") +validation_distributions <- list( + uniform = list(random = runif, density = dunif), + `beta-1-2` = list( + random = function(sample_size) rbeta(sample_size, 1, 2), + density = function(values) dbeta(values, 1, 2) + ), + `beta-0.75-2` = list( + random = function(sample_size) rbeta(sample_size, 0.75, 2), + density = function(values) dbeta(values, 0.75, 2) + ), + `beta-0.75-0.75` = list( + random = function(sample_size) rbeta(sample_size, 0.75, 0.75), + density = function(values) dbeta(values, 0.75, 0.75) + ) +) +evaluation_points <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.99, length.out = 301L), + 1 - 10^seq(-2, -10, length.out = 101L) +))) + +pdf(output_file, width = 12, height = 8) +par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) +for (sample_size in sort(unique(results$sample_size))) { + for (distribution in names(validation_distributions)) { + scenario_results <- results[ + results$sample_size == sample_size & + results$distribution == distribution, + ] + current_result <- scenario_results[scenario_results$method == "current", ] + selected_result <- scenario_results[scenario_results$method == "selected", ] + ratios <- c( + ISE = selected_result$global_ise / current_result$global_ise, + bias = selected_result$global_squared_bias / + current_result$global_squared_bias, + variance = selected_result$global_variance / + current_result$global_variance + ) + barplot( + ratios, col = c("grey45", "#E69F00", "#56B4E9"), + ylim = range(c(0, 1, ratios)), ylab = "selected / current", + main = sprintf("%s, n = %d", distribution, sample_size) + ) + abline(h = 1, lty = 2) + } +} +mtext( + sprintf("Selected estimator: %d paired replications", replication_count), + outer = TRUE, font = 2, cex = 1.1 +) + +par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) +for (sample_size in sort(unique(results$sample_size))) { + for (distribution in names(validation_distributions)) { + selected_result <- results[ + results$sample_size == sample_size & + results$distribution == distribution & + results$method == "selected", + ] + barplot( + rbind( + bulk = c(selected_result$lower_bulk_rate, selected_result$upper_bulk_rate), + finite = c( + selected_result$lower_finite_rate, + selected_result$upper_finite_rate + ) + ), + names.arg = c("lower", "upper"), col = c("grey60", "#0072B2"), + ylim = c(0, 1), ylab = "selection rate", + main = sprintf("%s, n = %d", distribution, sample_size) + ) + if (sample_size == min(results$sample_size) && + distribution == names(validation_distributions)[[1L]]) { + legend( + "topright", c("bulk", "finite"), + fill = c("grey60", "#0072B2"), bty = "n", cex = 0.75 + ) + } + } +} +mtext("Effective endpoint components", outer = TRUE, font = 2, cex = 1.1) + +sample_size <- 1000L +for (distribution_index in seq_along(validation_distributions)) { + true_density <- validation_distributions[[distribution_index]]$density( + evaluation_points + ) + par(mfrow = c(2, 3), mar = c(4, 4.2, 2.3, 0.6), oma = c(0, 0, 3, 0)) + for (replication in 1:2) { + set.seed( + 20260906L + 100000L * distribution_index + 1000L * 2L + replication + ) + observations <- validation_distributions[[distribution_index]]$random( + sample_size + ) + selected_fit <- fit_bounded_selected_estimator( + observations, + evaluation_points + ) + estimates <- list( + current = normalize_density( + evaluation_points, + dkde1d( + evaluation_points, + kde1d(observations, xmin = 0, xmax = 1) + ) + ), + selected = selected_fit$density + ) + plot( + evaluation_points, true_density, type = "l", lwd = 3, col = "black", + ylim = c(0, quantile(c(true_density, unlist(estimates)), 0.98)), + xlab = "x", ylab = "density", + main = sprintf( + "realization %d: L=%s, U=%s", + replication, + selected_fit$expert_choices[["lower"]], + selected_fit$expert_choices[["upper"]] + ) + ) + for (method in names(estimates)) { + lines( + evaluation_points, estimates[[method]], col = method_colors[[method]], + lwd = if (method == "selected") 2.5 else 1.5, + lty = match(method, names(estimates)) + ) + } + if (replication == 1L) { + legend( + "topright", c("truth", "current", "selected"), + col = c("black", method_colors), lty = c(1, 1, 2), + lwd = c(3, 1.5, 2.5), bty = "n", cex = 0.75 + ) + } + for (boundary in c("left", "right")) { + boundary_points <- if (boundary == "left") { + evaluation_points >= 1e-6 & evaluation_points <= 0.1 + } else { + evaluation_points >= 0.9 & evaluation_points <= 1 - 1e-6 + } + boundary_distances <- if (boundary == "left") { + evaluation_points[boundary_points] + } else { + 1 - evaluation_points[boundary_points] + } + boundary_order <- order(boundary_distances) + plot( + boundary_distances[boundary_order], + true_density[boundary_points][boundary_order], + type = "l", log = "x", lwd = 3, col = "black", + ylim = c(0, quantile(c( + true_density[boundary_points], + unlist(lapply(estimates, function(density) density[boundary_points])) + ), 0.99)), + xlab = "distance from boundary", ylab = "density", main = boundary + ) + for (method in names(estimates)) { + lines( + boundary_distances[boundary_order], + estimates[[method]][boundary_points][boundary_order], + col = method_colors[[method]], + lwd = if (method == "selected") 2.5 else 1.5, + lty = match(method, names(estimates)) + ) + } + } + } + mtext( + sprintf( + "%s, n = %d; effective choices shown in panel titles", + names(validation_distributions)[[distribution_index]], sample_size + ), + outer = TRUE, font = 2, cex = 1.1 + ) +} +dev.off() +message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R b/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R new file mode 100644 index 0000000..89b6a40 --- /dev/null +++ b/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R @@ -0,0 +1,234 @@ +# Plot the paired endpoint-classifier ablation and representative fits. +# Run from the root of the kde1d R package. + +if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { + stop("run from the kde1d package root with pkgload installed") +} +pkgload::load_all(".", quiet = TRUE) +source(paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", + "bounded_estimator.R" +)) + +arguments <- commandArgs(trailingOnly = TRUE) +input_file <- if (length(arguments) >= 1L) arguments[[1L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", + "endpoint-classifier-ablation.csv" +) +output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/plots/", + "endpoint-classifier-ablation.pdf" +) +if (length(arguments) > 2L) { + stop("usage: plot_endpoint_classifier_ablation.R [input.csv] [output.pdf]") +} + +results <- read.csv(input_file) +classifier_methods <- c( + "single-95", "single-1.5-95", "single-2-95", + "median-90", "vote-90", "vote-95" +) +method_labels <- c( + `single-95` = "1x", `single-1.5-95` = "1.5x", `single-2-95` = "2x", + `median-90` = "median", `vote-90` = "vote 90", `vote-95` = "vote 95" +) +method_colors <- c( + `single-95` = "#009E73", `single-1.5-95` = "#56B4E9", + `single-2-95` = "#E69F00", `median-90` = "#CC79A7", + `vote-90` = "#7B3294", `vote-95` = "#D55E00" +) +validation_distributions <- list( + uniform = list(random = runif, density = dunif), + `beta-1-2` = list( + random = function(sample_size) rbeta(sample_size, 1, 2), + density = function(values) dbeta(values, 1, 2) + ), + `beta-0.75-2` = list( + random = function(sample_size) rbeta(sample_size, 0.75, 2), + density = function(values) dbeta(values, 0.75, 2) + ), + `beta-0.75-0.75` = list( + random = function(sample_size) rbeta(sample_size, 0.75, 0.75), + density = function(values) dbeta(values, 0.75, 0.75) + ) +) +evaluation_points <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.99, length.out = 301L), + 1 - 10^seq(-2, -10, length.out = 101L) +))) + +dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) +pdf(output_file, width = 12, height = 8) + +par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) +for (sample_size in sort(unique(results$sample_size))) { + for (distribution in names(validation_distributions)) { + scenario_results <- results[ + results$sample_size == sample_size & + results$distribution == distribution, + ] + current_ise <- scenario_results$global_ise[ + scenario_results$method == "kde-current" + ] + scenario_results <- scenario_results[ + match(classifier_methods, scenario_results$method), + ] + ratios <- scenario_results$global_ise / current_ise + barplot( + ratios, + names.arg = method_labels[classifier_methods], + col = method_colors[classifier_methods], las = 2, cex.names = 0.7, + ylim = range(c(0, 1, ratios)), ylab = "global ISE / current", + main = sprintf("%s, n = %d", distribution, sample_size) + ) + abline(h = 1, lty = 2) + } +} +mtext( + sprintf( + "Classifier ISE: %d paired replications", + unique(results$replications) + ), + outer = TRUE, font = 2, cex = 1.1 +) + +par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) +for (sample_size in sort(unique(results$sample_size))) { + for (distribution in names(validation_distributions)) { + scenario_results <- results[ + results$sample_size == sample_size & + results$distribution == distribution & + results$method %in% classifier_methods, + ] + scenario_results <- scenario_results[ + match(classifier_methods, scenario_results$method), + ] + barplot( + rowMeans(scenario_results[, c("lower_accuracy", "upper_accuracy")]), + names.arg = method_labels[classifier_methods], + col = method_colors[classifier_methods], las = 2, cex.names = 0.7, + ylim = c(0, 1), ylab = "mean endpoint accuracy", + main = sprintf("%s, n = %d", distribution, sample_size) + ) + } +} +mtext( + "Classification accuracy (finite versus bulk endpoint component)", + outer = TRUE, font = 2, cex = 1.1 +) + +visual_methods <- c("single-95", "single-2-95", "vote-90") +sample_size <- 1000L +for (distribution_index in seq_along(validation_distributions)) { + true_density <- validation_distributions[[distribution_index]]$density( + evaluation_points + ) + par(mfrow = c(2, 3), mar = c(4, 4.2, 2.4, 0.6), oma = c(0, 0, 3, 0)) + for (replication in 1:2) { + set.seed( + 20260909L + 100000L * distribution_index + 1000L * 2L + replication + ) + observations <- validation_distributions[[distribution_index]]$random( + sample_size + ) + estimator_components <- fit_bounded_estimator_components( + observations, + evaluation_points + ) + selections <- list( + `single-95` = select_bounded_endpoint_experts_single_scale(observations), + `single-2-95` = select_bounded_endpoint_experts_single_scale( + observations, + tail_multiplier = 2 + ), + `vote-90` = select_bounded_endpoint_experts_multiscale( + observations, + evidence_threshold = qnorm(0.90), + rule = "vote" + ) + ) + estimates <- list( + current = normalize_density( + evaluation_points, + dkde1d( + evaluation_points, + kde1d(observations, xmin = 0, xmax = 1) + ) + ) + ) + for (method in visual_methods) { + estimator_components$selection <- selections[[method]] + estimates[[method]] <- fuse_bounded_estimator_components( + evaluation_points, + estimator_components + )$density + } + plot( + evaluation_points, true_density, type = "l", lwd = 3, col = "black", + ylim = c(0, quantile(c(true_density, unlist(estimates)), 0.98)), + xlab = "x", ylab = "density", + main = sprintf("realization %d", replication) + ) + lines(evaluation_points, estimates$current, col = "grey45", lwd = 1.5) + for (method in visual_methods) { + lines( + evaluation_points, estimates[[method]], col = method_colors[[method]], + lwd = if (method == "single-2-95") 2.5 else 1.5, + lty = match(method, visual_methods) + ) + } + if (replication == 1L) { + legend( + "topright", c("truth", "current", method_labels[visual_methods]), + col = c("black", "grey45", method_colors[visual_methods]), + lty = c(1, 1, seq_along(visual_methods)), + lwd = c(3, 1.5, 1.5, 2.5, 1.5), bty = "n", cex = 0.72 + ) + } + for (boundary in c("left", "right")) { + boundary_points <- if (boundary == "left") { + evaluation_points >= 1e-6 & evaluation_points <= 0.1 + } else { + evaluation_points >= 0.9 & evaluation_points <= 1 - 1e-6 + } + boundary_distances <- if (boundary == "left") { + evaluation_points[boundary_points] + } else { + 1 - evaluation_points[boundary_points] + } + boundary_order <- order(boundary_distances) + plot( + boundary_distances[boundary_order], + true_density[boundary_points][boundary_order], + type = "l", log = "x", lwd = 3, col = "black", + ylim = c(0, quantile(c( + true_density[boundary_points], + unlist(lapply(estimates, function(density) density[boundary_points])) + ), 0.98)), + xlab = "distance from boundary", ylab = "density", main = boundary + ) + lines( + boundary_distances[boundary_order], + estimates$current[boundary_points][boundary_order], + col = "grey45", lwd = 1.5 + ) + for (method in visual_methods) { + lines( + boundary_distances[boundary_order], + estimates[[method]][boundary_points][boundary_order], + col = method_colors[[method]], + lwd = if (method == "single-2-95") 2.5 else 1.5, + lty = match(method, visual_methods) + ) + } + } + } + mtext( + sprintf("%s, n = %d", names(validation_distributions)[distribution_index], sample_size), + outer = TRUE, font = 2, cex = 1.1 + ) +} + +dev.off() +message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R b/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R new file mode 100644 index 0000000..32cddd6 --- /dev/null +++ b/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R @@ -0,0 +1,195 @@ +# Paired validation of the selected bounded estimator against current kde1d. +# Run from the root of the kde1d R package. + +if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { + stop("run from the kde1d package root with pkgload installed") +} +pkgload::load_all(".", quiet = TRUE) +source(paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", + "bounded_estimator.R" +)) + +arguments <- commandArgs(trailingOnly = TRUE) +replication_count <- if (length(arguments) >= 1L) { + as.integer(arguments[[1L]]) +} else { + 100L +} +output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", + "bounded-estimator-validation.csv" +) +if (length(arguments) > 2L || !is.finite(replication_count) || + replication_count < 2L) { + stop("usage: validate_bounded_estimator.R [replications] [output.csv]") +} + +make_beta_distribution <- function(shape1, shape2) { + list( + random = function(sample_size) rbeta(sample_size, shape1, shape2), + density = function(values) dbeta(values, shape1, shape2) + ) +} +validation_distributions <- list( + uniform = list(random = runif, density = dunif), + `beta-1-2` = make_beta_distribution(1, 2), + `beta-0.75-2` = make_beta_distribution(0.75, 2), + `beta-0.75-0.75` = make_beta_distribution(0.75, 0.75) +) +sample_sizes <- c(100L, 1000L, 2000L) +methods <- c("current", "selected") +evaluation_points <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.99, length.out = 301L), + 1 - 10^seq(-2, -10, length.out = 101L) +))) +left_points <- evaluation_points <= 0.1 +right_points <- evaluation_points >= 0.9 +result_rows <- list() + +summarize_estimates <- function(estimates, true_density, region_points) { + mean_density <- rowMeans(estimates) + integrated_errors <- vapply( + seq_len(ncol(estimates)), + function(replication) { + trapezoid_integral( + evaluation_points[region_points], + (estimates[region_points, replication] - + true_density[region_points])^2 + ) + }, + numeric(1L) + ) + c( + ise = mean(integrated_errors), + ise_median = median(integrated_errors), + squared_bias = trapezoid_integral( + evaluation_points[region_points], + (mean_density[region_points] - true_density[region_points])^2 + ), + variance = trapezoid_integral( + evaluation_points[region_points], + rowMeans((estimates[region_points, , drop = FALSE] - + mean_density[region_points])^2) + ) + ) +} + +for (distribution_index in seq_along(validation_distributions)) { + true_density <- validation_distributions[[distribution_index]]$density( + evaluation_points + ) + for (sample_size in sample_sizes) { + estimates <- setNames( + lapply(methods, function(method) { + matrix(NA_real_, length(evaluation_points), replication_count) + }), + methods + ) + expert_choices <- array( + NA_character_, + dim = c(replication_count, 2L), + dimnames = list(NULL, c("lower", "upper")) + ) + for (replication in seq_len(replication_count)) { + set.seed( + 20260906L + 100000L * distribution_index + + 1000L * match(sample_size, sample_sizes) + replication + ) + observations <- validation_distributions[[distribution_index]]$random( + sample_size + ) + estimates$current[, replication] <- normalize_density( + evaluation_points, + dkde1d( + evaluation_points, + kde1d(observations, xmin = 0, xmax = 1) + ) + ) + estimator_components <- fit_bounded_estimator_components( + observations, + evaluation_points + ) + selected_fit <- fuse_bounded_estimator_components( + evaluation_points, + estimator_components + ) + estimates$selected[, replication] <- selected_fit$density + expert_choices[replication, ] <- selected_fit$expert_choices + } + for (method in methods) { + global_summary <- summarize_estimates( + estimates[[method]], + true_density, + rep(TRUE, length(evaluation_points)) + ) + left_summary <- summarize_estimates( + estimates[[method]], + true_density, + left_points + ) + right_summary <- summarize_estimates( + estimates[[method]], + true_density, + right_points + ) + result_rows[[length(result_rows) + 1L]] <- data.frame( + distribution = names(validation_distributions)[[distribution_index]], + sample_size = sample_size, + replications = replication_count, + method = method, + global_ise = global_summary[["ise"]], + global_ise_median = global_summary[["ise_median"]], + global_squared_bias = global_summary[["squared_bias"]], + global_variance = global_summary[["variance"]], + left_ise = left_summary[["ise"]], + left_squared_bias = left_summary[["squared_bias"]], + left_variance = left_summary[["variance"]], + right_ise = right_summary[["ise"]], + right_squared_bias = right_summary[["squared_bias"]], + right_variance = right_summary[["variance"]], + lower_finite_rate = if (method == "selected") { + mean(expert_choices[, "lower"] == "finite") + } else { + NA_real_ + }, + upper_finite_rate = if (method == "selected") { + mean(expert_choices[, "upper"] == "finite") + } else { + NA_real_ + }, + lower_bulk_rate = if (method == "selected") { + mean(expert_choices[, "lower"] == "bulk") + } else { + NA_real_ + }, + upper_bulk_rate = if (method == "selected") { + mean(expert_choices[, "upper"] == "bulk") + } else { + NA_real_ + }, + minimum_density = min(estimates[[method]]), + maximum_mass_error = max(abs(vapply( + seq_len(replication_count), + function(replication) { + trapezoid_integral( + evaluation_points, + estimates[[method]][, replication] + ) - 1 + }, + numeric(1L) + ))) + ) + } + message( + names(validation_distributions)[[distribution_index]], + ", n = ", sample_size + ) + } +} + +results <- do.call(rbind, result_rows) +dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) +write.csv(results, output_file, row.names = FALSE) +message("wrote ", normalizePath(output_file)) From a3968256b5d2bfd6c1fbf43e4b940be3cead8b33 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 13:52:57 +0200 Subject: [PATCH 03/25] Add one-sided boundary expert diagnostics --- diagnostic/README.md | 3 + diagnostic/one-sided-repair/HANDOFF.md | 33 ++ diagnostic/one-sided-repair/README.md | 44 +++ diagnostic/one-sided-repair/RESULTS.md | 59 +++ .../plots/local-floor-fraction-ablation.pdf | Bin 0 -> 77662 bytes .../results/local-floor-fraction-ablation.csv | 111 ++++++ .../scripts/ablate_local_floor_fraction.R | 212 +++++++++++ .../scripts/one_sided_estimator.R | 360 ++++++++++++++++++ .../plot_local_floor_fraction_ablation.R | 163 ++++++++ 9 files changed, 985 insertions(+) create mode 100644 diagnostic/one-sided-repair/HANDOFF.md create mode 100644 diagnostic/one-sided-repair/README.md create mode 100644 diagnostic/one-sided-repair/RESULTS.md create mode 100644 diagnostic/one-sided-repair/plots/local-floor-fraction-ablation.pdf create mode 100644 diagnostic/one-sided-repair/results/local-floor-fraction-ablation.csv create mode 100644 diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R create mode 100644 diagnostic/one-sided-repair/scripts/one_sided_estimator.R create mode 100644 diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R diff --git a/diagnostic/README.md b/diagnostic/README.md index 7466023..9624814 100644 --- a/diagnostic/README.md +++ b/diagnostic/README.md @@ -33,3 +33,6 @@ to zero. The separate transformation-boundary investigation, its retained simulation results, and its current recommendations live in [`boundary-repair/`](boundary-repair/README.md). + +The follow-up for supports with exactly one finite endpoint lives in +[`one-sided-repair/`](one-sided-repair/README.md). diff --git a/diagnostic/one-sided-repair/HANDOFF.md b/diagnostic/one-sided-repair/HANDOFF.md new file mode 100644 index 0000000..edf56af --- /dev/null +++ b/diagnostic/one-sided-repair/HANDOFF.md @@ -0,0 +1,33 @@ +# One-sided repair handoff + +The production branch already uses a scale-equivariant power-$3/4$ transform +for one-sided supports. The diagnostic candidate keeps that estimator as the +unweighted bulk and adds the selected two-boundary method's finite expert: +equal local-linear/local-quadratic estimates, a shrinking CDF gate, and a +$2\sqrt n$ order-statistic finite-versus-bulk decision. + +The bandwidth floor is the unweighted bandwidth fitted to the lowest 75% of +boundary distances. A 30-replication ablation compared fixed fractions from +15% through 100% and a $\sqrt n$ shrinking subset. Performance improved up to +75%; using all observations reversed the long-tail gains because remote Lomax +observations again controlled the floor. The 75% choice has mean global ISE +ratios to current of 0.902 at $n=100$ and 0.889 at $n=1000$, with corresponding +boundary ratios 0.854 and 0.834. + +The representative plots confirm that 75% removes most residual finite-endpoint +spiking. It is visually close to the full-sample floor for Exponential and +half-normal cases, but remains stable for Lomax. The main remaining loss is a +small-sample false finite classification for Gamma$(2)$: global ISE is 1.026 +and boundary ISE is 1.083 relative to current at $n=100$. At $n=1000$ the +classifier always chooses bulk for both Gamma examples, so the result is +exactly current. + +The log transform was rejected and removed. The working diagnostic now contains +only the current power-transform candidate and the floor-fraction validation. + +Before native C++ implementation, expand the scenario suite around the selected +75% value and classifier edge cases. In particular, add finite-boundary shapes +with steep nonzero slopes, heavier remote tails, upper-bounded reflections, and +sample sizes between 100 and 1000. Keep paired global/boundary ISE, bias, +variance, normalization, nonnegativity, reflection, scale, and realization +checks. diff --git a/diagnostic/one-sided-repair/README.md b/diagnostic/one-sided-repair/README.md new file mode 100644 index 0000000..66f7a1d --- /dev/null +++ b/diagnostic/one-sided-repair/README.md @@ -0,0 +1,44 @@ +# One-sided boundary repair + +This workspace applies the selected two-boundary idea to continuous densities +with exactly one known finite endpoint. It is deliberately separate from +`boundary-repair/`, which is stable. + +## Current candidate + +The power-$3/4$ transformation estimator is the unweighted bulk fit. A single +order-statistic tail index classifies the finite endpoint using +$k=\min(n-1,\lceil2\sqrt n\rceil)$ and the same 95% rule as in the +two-boundary estimator. A confidently finite endpoint receives the equal +local-linear/local-quadratic expert; exploding, vanishing, and ambiguous +endpoints reuse bulk. + +The boundary expert is blended with bulk through a smooth gate based on the +bulk CDF, with boundary probability $\min(0.25,n^{-1/2})$. Its local-polynomial +bandwidth is floored at the unweighted bandwidth fitted to the lowest 75% of +boundary distances. This preserves the stabilizing information in most of the +sample without allowing the most remote observations to dominate the floor. +The construction is reflection- and scale-equivariant. + +The validation suite uses 30 paired replications at $n=100,1000$ for +Exponential, half-normal, Gamma$(2)$, Gamma$(0.75)$, and Lomax$(2)$ densities. +The log transform was rejected and its experimental implementation and outputs +have been removed. + +## Files + +- `scripts/one_sided_estimator.R`: current R reference implementation. +- `scripts/ablate_local_floor_fraction.R`: selected floor-fraction ablation. +- `scripts/plot_local_floor_fraction_ablation.R`: tuning curves and example + estimates. +- `results/local-floor-fraction-ablation.csv` and + `plots/local-floor-fraction-ablation.pdf`: current tuning evidence. +- `RESULTS.md`: numerical conclusions. +- `HANDOFF.md`: implementation state and next steps. + +Run from the R-package root: + +```sh +Rscript inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R 30 +Rscript inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R +``` diff --git a/diagnostic/one-sided-repair/RESULTS.md b/diagnostic/one-sided-repair/RESULTS.md new file mode 100644 index 0000000..b302222 --- /dev/null +++ b/diagnostic/one-sided-repair/RESULTS.md @@ -0,0 +1,59 @@ +# One-sided boundary-repair results + +## Estimator held fixed during the ablation + +The candidate uses the power-$3/4$ estimator as unweighted bulk. If the +order-statistic classifier identifies a finite nonzero endpoint, equal +local-linear and local-quadratic estimates are blended into the shrinking +boundary region. Only the bandwidth-floor sample fraction changes. + +The experiment uses 30 paired replications for five densities at $n=100$ and +$n=1000$. It compares the lowest 15%, 20%, 25%, 30%, 35%, 40%, 50%, 75%, and +100% of boundary distances, plus a shrinking subset of $\lceil\sqrt n\rceil$ +distances. All values below are candidate/current ratios, so smaller is better. + +## Aggregate result + +| $n$ | floor subset | global ISE | boundary ISE | squared bias | variance | +|---:|---:|---:|---:|---:|---:| +| 100 | 25% | 0.989 | 0.986 | 0.895 | 1.007 | +| 100 | 50% | 0.933 | 0.899 | 0.860 | 0.949 | +| 100 | 75% | **0.902** | **0.854** | **0.829** | **0.917** | +| 100 | 100% | 0.941 | 0.911 | 1.004 | 0.923 | +| 100 | $\sqrt n$ | 1.073 | 1.127 | 0.905 | 1.102 | +| 1000 | 25% | 0.933 | 0.896 | 0.801 | 0.976 | +| 1000 | 50% | 0.909 | 0.863 | 0.797 | 0.946 | +| 1000 | 75% | **0.889** | **0.834** | **0.789** | **0.924** | +| 1000 | 100% | 0.983 | 0.959 | 0.963 | 0.986 | +| 1000 | $\sqrt n$ | 1.043 | 1.064 | 0.806 | 1.112 | + +The old 25% floor is too local. Increasing the subset through 75% reduces both +bias and variance. A shrinking $\sqrt n$ subset is clearly too small and +reintroduces instability. Using the full sample overshoots the optimum because +remote tail observations again inflate the floor. + +## Selected 75% floor by density + +| density | $n$ | global ISE | boundary ISE | squared bias | variance | +|---|---:|---:|---:|---:|---:| +| Exponential | 100 | 0.808 | 0.709 | 0.575 | 0.841 | +| Exponential | 1000 | 0.805 | 0.722 | 0.455 | 0.890 | +| half-normal | 100 | 0.869 | 0.744 | 0.817 | 0.878 | +| half-normal | 1000 | 0.808 | 0.672 | 0.868 | 0.801 | +| Gamma$(2)$ | 100 | 1.026 | 1.083 | 1.174 | 1.019 | +| Gamma$(2)$ | 1000 | 1.000 | 1.000 | 1.000 | 1.000 | +| Gamma$(0.75)$ | 100 | 0.985 | 0.983 | 0.913 | 0.992 | +| Gamma$(0.75)$ | 1000 | 1.000 | 1.000 | 1.000 | 1.000 | +| Lomax$(2)$ | 100 | 0.819 | 0.752 | 0.670 | 0.857 | +| Lomax$(2)$ | 1000 | 0.833 | 0.774 | 0.622 | 0.926 | + +The full-sample floor would improve the finite light-tail cases further, but it +raises Lomax global ISE to 1.075 at $n=100$ and 1.392 at $n=1000$. The 75% +floor retains large improvements for both light and long remote tails and is +therefore the selected default. + +The realization plots show the same trade-off. Relative to 25%, the selected +floor substantially calms the near-endpoint estimates. Relative to 100%, it +avoids the flattened Lomax boundary while remaining visually smooth for +Exponential data. All simulated estimates are nonnegative and normalized to +numerical precision. diff --git a/diagnostic/one-sided-repair/plots/local-floor-fraction-ablation.pdf b/diagnostic/one-sided-repair/plots/local-floor-fraction-ablation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1fafa4a0116d914812a2ef0062d64719a4959a6a GIT binary patch literal 77662 zcmagE2Ut_z(l_egMp0BijDirPDj*T0SLrIvMu(uGNbjK&L{X$S0TBUdf|OwBgaicX zMT$UxP^1K;_fFuh=sD*-?{}Yjzvp4r-fQ;EteM};n!OUj{XkjurjVcrEqA~~z+^yY zz)xcrS|RpZ?2ZTpnE|jMtf?|RcQ-9WSq_A$# z%E{4MIG9ts5dM!h?64>>Qu7!yY_)ZsE#)8wfmN{~rbM|Ca(qjw0=1 z;o$Z!ahQ^$gBzH-vP=9?hdr`zbws+D0ed3N8fdMb+8|Ed+KawoZW9WBbQ5+w0?I-93^~xr=oQn<8+q$9FqX?c_)Xi zHO@!HZEI!c*li8zBCB+cbO=d=F;;`k^^xh#5&vqRjB3fD%dBA!*Vcb0`8(!|JtS9q zZD$D2*_rhj?JScUndv%@O7Gn>%6O?RrG_lMp&*@oT;?@2;S;IkJRf_=%c56fN$(1E zg0_Ystp8Yq?{KrL?Z~R`K62~0u9uysC- zr`^w44nvn8!-w+_eIqar$Wwi^z9y9i2glS2ALb0_(c zzuMEJP&K<-6@G2m;r1m%r>$AHzPkUIH_t*2HDP(|LrMgF^!G0cWdxRre*aipF!$)! 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+"lomax_2",1000,30,"fixed-100pct",0.00649334812218761,0.00215366087792471,0.0043396872442629,0.00536551738685692,0.00189185791667889,0.00347365947017803,0.666666666666667,316.351208853879,0,1.11022302462516e-16 +"lomax_2",1000,30,"shrinking",0.00485525856366109,0.000865000667250043,0.00399025789641104,0.00369570145755347,0.000550680684486621,0.00314502077306685,0.666666666666667,1.32912073570791,0,1.11022302462516e-16 diff --git a/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R b/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R new file mode 100644 index 0000000..ec0bd78 --- /dev/null +++ b/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R @@ -0,0 +1,212 @@ +# Paired ablation of the local probability mass used for the bandwidth floor. +# Run from the root of the kde1d R package. + +if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { + stop("run from the kde1d package root with pkgload installed") +} +pkgload::load_all(".", quiet = TRUE) +source(paste0( + "inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/", + "one_sided_estimator.R" +)) + +arguments <- commandArgs(trailingOnly = TRUE) +replication_count <- if (length(arguments) >= 1L) { + as.integer(arguments[[1L]]) +} else { + 30L +} +output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( + "inst/include/kde1d-cpp/diagnostic/one-sided-repair/results/", + "local-floor-fraction-ablation.csv" +) +if (length(arguments) > 2L || !is.finite(replication_count) || + replication_count < 2L) { + stop("usage: ablate_local_floor_fraction.R [replications] [output.csv]") +} + +validation_distributions <- list( + exponential = list(random = rexp, density = dexp, quantile = qexp), + half_normal = list( + random = function(sample_size) abs(rnorm(sample_size)), + density = function(values) 2 * dnorm(values), + quantile = function(probabilities) qnorm((probabilities + 1) / 2) + ), + gamma_2 = list( + random = function(sample_size) rgamma(sample_size, 2), + density = function(values) dgamma(values, 2), + quantile = function(probabilities) qgamma(probabilities, 2) + ), + gamma_0.75 = list( + random = function(sample_size) rgamma(sample_size, 0.75), + density = function(values) dgamma(values, 0.75), + quantile = function(probabilities) qgamma(probabilities, 0.75) + ), + lomax_2 = list( + random = function(sample_size) (1 - runif(sample_size))^(-0.5) - 1, + density = function(values) 2 / (1 + values)^3, + quantile = function(probabilities) (1 - probabilities)^(-0.5) - 1 + ) +) +sample_sizes <- c(100L, 1000L) +local_floor_fractions <- c( + 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.50, 0.75, 1 +) +fraction_methods <- paste0( + "fixed-", + format(100 * local_floor_fractions, trim = TRUE), + "pct" +) +candidate_methods <- c(fraction_methods, "shrinking") +methods <- c("current", candidate_methods) +evaluation_probabilities <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.999, length.out = 401L), + 0.9999, 0.99999 +))) +result_rows <- list() + +summarize_fraction_estimates <- function( + evaluation_points, + estimates, + true_density, + region_points) { + mean_density <- rowMeans(estimates) + integrated_errors <- vapply(seq_len(ncol(estimates)), function(replication) { + one_sided_trapezoid_integral( + evaluation_points[region_points], + (estimates[region_points, replication] - true_density[region_points])^2 + ) + }, numeric(1L)) + c( + ise = mean(integrated_errors), + squared_bias = one_sided_trapezoid_integral( + evaluation_points[region_points], + (mean_density[region_points] - true_density[region_points])^2 + ), + variance = one_sided_trapezoid_integral( + evaluation_points[region_points], + rowMeans((estimates[region_points, , drop = FALSE] - + mean_density[region_points])^2) + ) + ) +} + +for (distribution_index in seq_along(validation_distributions)) { + evaluation_points <- validation_distributions[[distribution_index]]$quantile( + evaluation_probabilities + ) + true_density <- validation_distributions[[distribution_index]]$density( + evaluation_points + ) + boundary_points <- evaluation_probabilities <= 0.1 + for (sample_size in sample_sizes) { + estimates <- setNames(lapply(methods, function(method) { + matrix(NA_real_, length(evaluation_points), replication_count) + }), methods) + finite_choices <- logical(replication_count) + floor_ratios <- setNames(lapply(candidate_methods, function(method) { + rep(NA_real_, replication_count) + }), candidate_methods) + for (replication in seq_len(replication_count)) { + set.seed( + 20260914L + 100000L * distribution_index + + 1000L * match(sample_size, sample_sizes) + replication + ) + observations <- validation_distributions[[distribution_index]]$random( + sample_size + ) + estimates$current[, replication] <- normalize_one_sided_density( + evaluation_points, + dkde1d(evaluation_points, kde1d(observations, xmin = 0)) + ) + for (fraction_index in seq_along(local_floor_fractions)) { + method <- fraction_methods[[fraction_index]] + candidate_fit <- fit_one_sided_candidate( + observations, + evaluation_points, + bandwidth_floor = "local", + local_floor_fraction = local_floor_fractions[[fraction_index]] + ) + estimates[[method]][, replication] <- candidate_fit$density + floor_ratios[[method]][[replication]] <- mean( + candidate_fit$boundary_bandwidths / + candidate_fit$selected_boundary_bandwidths + ) + if (fraction_index == 1L) { + finite_choices[[replication]] <- + candidate_fit$expert_choice == "finite" + } + } + shrinking_fit <- fit_one_sided_candidate( + observations, + evaluation_points, + bandwidth_floor = "shrinking" + ) + estimates$shrinking[, replication] <- shrinking_fit$density + floor_ratios$shrinking[[replication]] <- mean( + shrinking_fit$boundary_bandwidths / + shrinking_fit$selected_boundary_bandwidths + ) + } + for (method in methods) { + global_summary <- summarize_fraction_estimates( + evaluation_points, + estimates[[method]], + true_density, + rep(TRUE, length(evaluation_points)) + ) + boundary_summary <- summarize_fraction_estimates( + evaluation_points, + estimates[[method]], + true_density, + boundary_points + ) + result_rows[[length(result_rows) + 1L]] <- data.frame( + distribution = names(validation_distributions)[[distribution_index]], + sample_size = sample_size, + replications = replication_count, + method = method, + global_ise = global_summary[["ise"]], + global_squared_bias = global_summary[["squared_bias"]], + global_variance = global_summary[["variance"]], + boundary_ise = boundary_summary[["ise"]], + boundary_squared_bias = boundary_summary[["squared_bias"]], + boundary_variance = boundary_summary[["variance"]], + finite_rate = if (method %in% candidate_methods) { + mean(finite_choices) + } else { + NA_real_ + }, + mean_floor_ratio = if ( + method %in% candidate_methods && + any(is.finite(floor_ratios[[method]])) + ) { + mean(floor_ratios[[method]], na.rm = TRUE) + } else { + NA_real_ + }, + minimum_density = min(estimates[[method]]), + maximum_mass_error = max(abs(vapply( + seq_len(replication_count), + function(replication) { + one_sided_trapezoid_integral( + evaluation_points, + estimates[[method]][, replication] + ) - 1 + }, + numeric(1L) + ))) + ) + } + message( + names(validation_distributions)[[distribution_index]], + ", n = ", sample_size + ) + } +} + +results <- do.call(rbind, result_rows) +dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) +write.csv(results, output_file, row.names = FALSE) +message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/one-sided-repair/scripts/one_sided_estimator.R b/diagnostic/one-sided-repair/scripts/one_sided_estimator.R new file mode 100644 index 0000000..8a9ec0b --- /dev/null +++ b/diagnostic/one-sided-repair/scripts/one_sided_estimator.R @@ -0,0 +1,360 @@ +# Reference R implementation of the one-sided finite-boundary candidate. + +one_sided_trapezoid_integral <- function(evaluation_points, values) { + sum(diff(evaluation_points) * + (values[-length(values)] + values[-1L]) / 2) +} + +normalize_one_sided_density <- function(evaluation_points, density) { + density <- pmax(0, density) + density_mass <- one_sided_trapezoid_integral(evaluation_points, density) + if (!is.finite(density_mass) || density_mass <= 0) { + stop("density cannot be normalized") + } + density / density_mass +} + +one_sided_smoothstep <- function(normalized_distance) { + 3 * normalized_distance^2 - 2 * normalized_distance^3 +} + +make_one_sided_expert_weights <- function(probabilities, sample_size, + concentration = 1, + shrinkage_exponent = 0.5) { + boundary_fraction <- min( + 0.25, + concentration / sample_size^shrinkage_exponent + ) + boundary_weights <- 1 - one_sided_smoothstep(pmin( + 1, + probabilities / boundary_fraction + )) + cbind(boundary = boundary_weights, bulk = 1 - boundary_weights) +} + +one_sided_weighted_quantile <- function(values, weights, probability) { + value_order <- order(values) + ordered_weights <- weights[value_order] + values[value_order][which( + cumsum(ordered_weights) / sum(ordered_weights) >= probability + )[[1L]]] +} + +select_one_sided_bandwidth_floor <- function( + boundary_distances, + bandwidth_weights, + degree, + bandwidth_floor = c("local", "shrinking", "global", "none", "robust"), + local_floor_fraction = 0.75) { + bandwidth_floor <- match.arg(bandwidth_floor) + if (bandwidth_floor == "none") { + return(0) + } + if (bandwidth_floor == "global") { + return(kde1d(boundary_distances, deg = degree)$bw) + } + if (bandwidth_floor == "local" || bandwidth_floor == "shrinking") { + if (!is.finite(local_floor_fraction) || local_floor_fraction <= 0 || + local_floor_fraction > 1) { + stop("local_floor_fraction must lie in (0, 1]") + } + local_count <- if (bandwidth_floor == "shrinking") { + max(4L, ceiling(sqrt(length(boundary_distances)))) + } else { + max(4L, ceiling(local_floor_fraction * length(boundary_distances))) + } + return(kde1d(sort(boundary_distances)[seq_len(local_count)], deg = degree)$bw) + } + weighted_median <- one_sided_weighted_quantile( + boundary_distances, + bandwidth_weights, + 0.5 + ) + weighted_mad <- one_sided_weighted_quantile( + abs(boundary_distances - weighted_median), + bandwidth_weights, + 0.5 + ) + if (!(weighted_mad > 0)) { + weighted_mad <- one_sided_weighted_quantile( + boundary_distances, + bandwidth_weights, + 0.75 + ) - weighted_median + } + if (!(weighted_mad > 0)) { + weighted_mad <- max(boundary_distances) * .Machine$double.eps + } + winsorized_distances <- pmin( + boundary_distances, + weighted_median + 6 * weighted_mad + ) + kde1d(winsorized_distances, deg = degree)$bw +} + +fit_one_sided_bulk <- function( + observations, + evaluation_points, + lower_bound, + upper_bound) { + lower_bounded <- !is.na(lower_bound) + bulk_model <- if (lower_bounded) { + kde1d(observations, xmin = lower_bound) + } else { + kde1d(observations, xmax = upper_bound) + } + list( + density = normalize_one_sided_density( + evaluation_points, + dkde1d(evaluation_points, bulk_model) + ), + boundary_probabilities = if (lower_bounded) { + pkde1d(evaluation_points, bulk_model) + } else { + 1 - pkde1d(evaluation_points, bulk_model) + } + ) +} + +fit_one_sided_local_polynomial <- function( + boundary_distances, + evaluation_distances, + bandwidth_weights, + minimum_bandwidth, + degree) { + if (!degree %in% c(1, 2)) { + stop("local boundary degree must be 1 or 2") + } + selected_bandwidth <- kde1d( + boundary_distances, + weights = bandwidth_weights, + deg = degree + )$bw + bandwidth <- max(selected_bandwidth, minimum_bandwidth) + standardized_boundary <- evaluation_distances / bandwidth + truncated_moment_0 <- pnorm(standardized_boundary) + truncated_moment_1 <- -dnorm(standardized_boundary) + truncated_moment_2 <- truncated_moment_0 - + standardized_boundary * dnorm(standardized_boundary) + if (degree == 1) { + moment_determinant <- truncated_moment_0 * truncated_moment_2 - + truncated_moment_1^2 + equivalent_kernel_coefficients <- cbind( + truncated_moment_2 / moment_determinant, + -truncated_moment_1 / moment_determinant + ) + } else { + truncated_moment_3 <- -( + standardized_boundary^2 + 2 + ) * dnorm(standardized_boundary) + truncated_moment_4 <- 3 * truncated_moment_0 - ( + standardized_boundary^3 + 3 * standardized_boundary + ) * dnorm(standardized_boundary) + moment_determinant <- + truncated_moment_0 * ( + truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 + ) - + truncated_moment_1 * ( + truncated_moment_1 * truncated_moment_4 - + truncated_moment_2 * truncated_moment_3 + ) + + truncated_moment_2 * ( + truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 + ) + equivalent_kernel_coefficients <- cbind( + ( + truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 + ) / moment_determinant, + ( + truncated_moment_2 * truncated_moment_3 - + truncated_moment_1 * truncated_moment_4 + ) / moment_determinant, + ( + truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 + ) / moment_determinant + ) + } + density <- numeric(length(evaluation_distances)) + for (chunk_start in seq(1L, length(evaluation_distances), by = 128L)) { + chunk_indices <- chunk_start:min( + chunk_start + 127L, + length(evaluation_distances) + ) + kernel_arguments <- outer( + evaluation_distances[chunk_indices], + boundary_distances, + "-" + ) / bandwidth + base_kernels <- dnorm(kernel_arguments) + corrected_kernels <- base_kernels * + equivalent_kernel_coefficients[chunk_indices, 1L] + for (polynomial_order in seq_len(degree)) { + corrected_kernels <- corrected_kernels + + base_kernels * + equivalent_kernel_coefficients[ + chunk_indices, + polynomial_order + 1L + ] * kernel_arguments^polynomial_order + } + density[chunk_indices] <- rowMeans(corrected_kernels) / bandwidth + } + list( + density = normalize_one_sided_density(evaluation_distances, density), + bandwidth = bandwidth, + selected_bandwidth = selected_bandwidth + ) +} + +select_one_sided_endpoint_expert <- function( + boundary_distances, + tail_multiplier = 2, + evidence_threshold = qnorm(0.95), + minimum_finite_index = 0.9) { + tail_count <- min( + length(boundary_distances) - 1L, + ceiling(tail_multiplier * sqrt(length(boundary_distances))) + ) + ordered_distances <- sort(boundary_distances) + tail_index <- tail_count / sum(log( + ordered_distances[[tail_count + 1L]] / + pmax(.Machine$double.eps, ordered_distances[seq_len(tail_count)]) + )) + list( + expert_choice = if ( + tail_index >= minimum_finite_index && + tail_index * (1 - evidence_threshold / sqrt(tail_count)) <= 1 + ) { + "finite" + } else { + "bulk" + }, + tail_index = tail_index, + tail_count = tail_count + ) +} + +fit_one_sided_candidate <- function( + observations, + evaluation_points, + lower_bound = 0, + upper_bound = NA_real_, + concentration = 1, + shrinkage_exponent = 0.5, + bandwidth_floor = c("local", "shrinking", "global", "none", "robust"), + local_floor_fraction = 0.75) { + bandwidth_floor <- match.arg(bandwidth_floor) + if (is.na(lower_bound) == is.na(upper_bound)) { + stop("exactly one finite boundary must be supplied") + } + if (length(observations) < 4L || any(!is.finite(observations)) || + any(!is.finite(evaluation_points)) || + is.unsorted(evaluation_points, strictly = TRUE)) { + stop("observations and evaluation_points must be finite and ordered") + } + lower_bounded <- !is.na(lower_bound) + boundary_distances <- if (lower_bounded) { + observations - lower_bound + } else { + upper_bound - observations + } + if (any(boundary_distances < 0)) { + stop("observations must lie inside the supplied support") + } + evaluation_distances <- if (lower_bounded) { + evaluation_points - lower_bound + } else { + rev(upper_bound - evaluation_points) + } + bulk_fit <- fit_one_sided_bulk( + observations, + evaluation_points, + lower_bound, + upper_bound + ) + selection <- select_one_sided_endpoint_expert(boundary_distances) + if (selection$expert_choice == "bulk") { + return(list( + density = bulk_fit$density, + expert_choice = "bulk", + tail_index = selection$tail_index, + tail_count = selection$tail_count, + boundary_bandwidths = c(linear = NA_real_, quadratic = NA_real_), + selected_boundary_bandwidths = c( + linear = NA_real_, quadratic = NA_real_ + ), + bandwidth_floor = bandwidth_floor, + local_floor_fraction = local_floor_fraction, + boundary_fraction = min( + 0.25, + concentration / length(observations)^shrinkage_exponent + ) + )) + } + probability_ranks <- (rank( + boundary_distances, + ties.method = "average" + ) - 0.5) / length(observations) + bandwidth_weights <- make_one_sided_expert_weights( + probability_ranks, + length(observations), + concentration, + shrinkage_exponent + )[, "boundary"] + local_fits <- lapply(c(1L, 2L), function(degree) { + fit_one_sided_local_polynomial( + boundary_distances, + evaluation_distances, + bandwidth_weights, + select_one_sided_bandwidth_floor( + boundary_distances, + bandwidth_weights, + degree, + bandwidth_floor, + local_floor_fraction + ), + degree + ) + }) + boundary_density <- rowMeans(vapply( + local_fits, + function(local_fit) local_fit$density, + numeric(length(evaluation_distances)) + )) + if (!lower_bounded) { + boundary_density <- rev(boundary_density) + } + evaluation_weights <- make_one_sided_expert_weights( + bulk_fit$boundary_probabilities, + length(observations), + concentration, + shrinkage_exponent + ) + list( + density = normalize_one_sided_density( + evaluation_points, + evaluation_weights[, "boundary"] * boundary_density + + evaluation_weights[, "bulk"] * bulk_fit$density + ), + expert_choice = "finite", + tail_index = selection$tail_index, + tail_count = selection$tail_count, + boundary_bandwidths = setNames( + vapply(local_fits, function(local_fit) local_fit$bandwidth, numeric(1L)), + c("linear", "quadratic") + ), + selected_boundary_bandwidths = setNames( + vapply( + local_fits, + function(local_fit) local_fit$selected_bandwidth, + numeric(1L) + ), + c("linear", "quadratic") + ), + bandwidth_floor = bandwidth_floor, + local_floor_fraction = local_floor_fraction, + boundary_fraction = min( + 0.25, + concentration / length(observations)^shrinkage_exponent + ) + ) +} diff --git a/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R b/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R new file mode 100644 index 0000000..ce84da5 --- /dev/null +++ b/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R @@ -0,0 +1,163 @@ +# Plot the local bandwidth-floor fraction ablation. +# Run from the root of the kde1d R package. + +if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { + stop("run from the kde1d package root with pkgload installed") +} +pkgload::load_all(".", quiet = TRUE) +source(paste0( + "inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/", + "one_sided_estimator.R" +)) + +input_file <- paste0( + "inst/include/kde1d-cpp/diagnostic/one-sided-repair/results/", + "local-floor-fraction-ablation.csv" +) +output_file <- paste0( + "inst/include/kde1d-cpp/diagnostic/one-sided-repair/plots/", + "local-floor-fraction-ablation.pdf" +) +results <- read.csv(input_file) +fractions <- as.numeric(sub( + "pct$", "", sub("fixed-", "", results$method[grepl("^fixed", results$method)]), + fixed = FALSE +)) +fractions <- sort(unique(fractions)) +comparison_distributions <- list( + exponential = list(random = rexp, density = dexp, quantile = qexp), + gamma_2 = list( + random = function(sample_size) rgamma(sample_size, 2), + density = function(values) dgamma(values, 2), + quantile = function(probabilities) qgamma(probabilities, 2) + ), + lomax_2 = list( + random = function(sample_size) (1 - runif(sample_size))^(-0.5) - 1, + density = function(values) 2 / (1 + values)^3, + quantile = function(probabilities) (1 - probabilities)^(-0.5) - 1 + ) +) +evaluation_probabilities <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.999, length.out = 401L), + 0.9999, 0.99999 +))) +method_colors <- c( + current = "grey45", `25%` = "#0072B2", `75%` = "#009E73", + `100%` = "#D55E00" +) + +dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) +pdf(output_file, width = 11, height = 7.5) +par(mfrow = c(2, 2), mar = c(4.3, 4.5, 2.3, 0.8), oma = c(0, 0, 3, 0)) +for (sample_size in sort(unique(results$sample_size))) { + current_results <- results[ + results$sample_size == sample_size & results$method == "current", + ] + fixed_results <- results[ + results$sample_size == sample_size & grepl("^fixed", results$method), + ] + fixed_results <- merge( + fixed_results, + current_results[, c("distribution", "global_ise", "boundary_ise")], + by = "distribution", suffixes = c("", "_current") + ) + for (metric in c("global", "boundary")) { + ratio_matrix <- vapply(fractions, function(fraction) { + selected_results <- fixed_results[ + fixed_results$method == paste0("fixed-", fraction, "pct"), + ] + selected_results[[paste0(metric, "_ise")]] / + selected_results[[paste0(metric, "_ise_current")]] + }, numeric(nrow(current_results))) + matplot( + fractions, t(ratio_matrix), type = "l", lty = 1, lwd = 1.4, + col = adjustcolor("grey40", 0.45), ylim = range(c(0.7, 1.1, ratio_matrix)), + xlab = "lowest sample fraction used for floor (%)", + ylab = "candidate / current ISE", + main = sprintf("%s ISE, n=%d", metric, sample_size) + ) + lines(fractions, colMeans(ratio_matrix), lwd = 3, col = "#009E73") + abline(h = 1, lty = 2) + } +} +mtext("Bandwidth-floor fraction: density-specific curves and mean", outer = TRUE, + font = 2, cex = 1.1) + +for (boundary_zoom in c(FALSE, TRUE)) { + par(mfrow = c(2, 3), mar = c(4.2, 4.2, 2.5, 0.5), oma = c(0, 0, 3, 0)) + for (sample_size in c(100L, 1000L)) { + for (distribution_index in seq_along(comparison_distributions)) { + evaluation_points <- comparison_distributions[[distribution_index]]$quantile( + evaluation_probabilities + ) + true_density <- comparison_distributions[[distribution_index]]$density( + evaluation_points + ) + set.seed( + 20260914L + 100000L * match( + names(comparison_distributions)[[distribution_index]], + c("exponential", "half_normal", "gamma_2", "gamma_0.75", "lomax_2") + ) + 1000L * match(sample_size, c(100L, 1000L)) + 1L + ) + observations <- comparison_distributions[[distribution_index]]$random( + sample_size + ) + estimates <- list( + current = normalize_one_sided_density( + evaluation_points, + dkde1d(evaluation_points, kde1d(observations, xmin = 0)) + ), + `25%` = fit_one_sided_candidate( + observations, evaluation_points, local_floor_fraction = 0.25 + )$density, + `75%` = fit_one_sided_candidate( + observations, evaluation_points, local_floor_fraction = 0.75 + )$density, + `100%` = fit_one_sided_candidate( + observations, evaluation_points, local_floor_fraction = 1 + )$density + ) + plotted_points <- if (boundary_zoom) { + evaluation_probabilities <= 0.2 + } else { + evaluation_probabilities <= 0.999 + } + plot( + evaluation_points[plotted_points], true_density[plotted_points], + type = "l", lwd = 3, col = "black", log = if (boundary_zoom) "x" else "", + ylim = c(0, quantile(c( + true_density[plotted_points], + unlist(lapply(estimates, function(density) density[plotted_points])) + ), 0.995)), + xlab = if (boundary_zoom) "distance from boundary" else "x", + ylab = "density", + main = sprintf( + "%s, n=%d", names(comparison_distributions)[[distribution_index]], + sample_size + ) + ) + for (method in names(estimates)) { + lines( + evaluation_points[plotted_points], estimates[[method]][plotted_points], + col = method_colors[[method]], lwd = if (method == "75%") 2.5 else 1.5, + lty = match(method, names(estimates)) + ) + } + if (sample_size == 100L && distribution_index == 1L) { + legend( + "topright", c("truth", names(estimates)), + col = c("black", method_colors), lty = c(1, seq_along(estimates)), + lwd = c(3, 1.5, 1.5, 2.5, 1.5), bty = "n", cex = 0.72 + ) + } + } + } + mtext( + if (boundary_zoom) "Representative boundary views" else + "Representative full-density views", + outer = TRUE, font = 2, cex = 1.1 + ) +} +dev.off() +message("wrote ", normalizePath(output_file)) From d6b78339121bb7ccf18c7b6073161a15b195362e Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 14:48:28 +0200 Subject: [PATCH 04/25] Document native boundary expert roadmap --- diagnostic/boundary-repair/NATIVE_CPP.md | 89 +---- diagnostic/boundary-repair/README.md | 2 +- diagnostic/one-sided-repair/NATIVE_CPP.md | 425 ++++++++++++++++++++++ diagnostic/one-sided-repair/README.md | 1 + 4 files changed, 430 insertions(+), 87 deletions(-) create mode 100644 diagnostic/one-sided-repair/NATIVE_CPP.md diff --git a/diagnostic/boundary-repair/NATIVE_CPP.md b/diagnostic/boundary-repair/NATIVE_CPP.md index 1672e4a..45608d8 100644 --- a/diagnostic/boundary-repair/NATIVE_CPP.md +++ b/diagnostic/boundary-repair/NATIVE_CPP.md @@ -1,88 +1,5 @@ # Native C++ implementation plan -## Integration point - -The production estimator belongs in -`include/kde1d/kde1d.hpp`, where `Kde1d::fit()` currently handles bounded -continuous data through a single probit-transformed local-likelihood fit. The -new path should activate only when both bounds are finite and the variable is -continuous. One-sided, unbounded, discrete, and zero-inflated behavior should -remain unchanged. - -Avoid implementing the method through recursively constructed public -`Kde1d` objects: a nested bounded fit would activate the boundary selector -again. Extract the existing bounded-probit calculation into a private helper, -or introduce an internal mode that requests the legacy transformation fit -directly. - -## Components to implement - -1. Normalize observations and grid locations to $[0,1]$ using the supplied - finite support. Convert final density values back with the inverse support - length. This must preserve affine equivariance. -2. Fit the unweighted legacy probit bulk estimator once. Retain its PDF, CDF, - and final original-scale grid. -3. Compute $k=\min(n-1,\lceil2\sqrt n\rceil)$ and the two order-statistic tail - indices. Use a partial selection algorithm if convenient, although a full - sort is acceptable initially. Protect zero endpoint distances with the C++ - equivalent of `std::numeric_limits::epsilon()`. -4. Classify each endpoint as finite or bulk using the fixed finite-endpoint - rule in `README.md`. Exploding, vanishing, and ambiguous cases all use bulk. -5. Construct rank-based lower and upper bandwidth weights using average ranks - for ties and boundary fraction $\min(0.25,n^{-1/2})$. -6. Add a private Gaussian equivalent-kernel evaluator for boundary polynomial - degrees one and two. Select each bandwidth through - `bandwidth::PluginBandwidthSelector` with endpoint weights, impose the - corresponding full-sample unweighted bandwidth as its floor, but evaluate - density contributions with equal observation weights. Reflect data and - grid locations for the upper endpoint. -7. Average the degree-one and degree-two endpoint densities. Clamp negative - component values to zero before component normalization, matching the R - reference. -8. Obtain fusion probabilities from the bulk CDF and evaluate the smoothstep - gates. Substitute bulk or finite component values according to each - endpoint decision, fuse arithmetically, clamp at zero, and normalize on the - final grid. -9. Store the fused values in `interp::InterpolationGrid` so existing PDF, - CDF, quantile, and simulation methods continue to work without a new - public fitted-object representation. - -## API and metadata decisions - -The first implementation can keep the method automatic for two finite bounds, -but an internal feature switch is useful while validating. Decide whether the -selector threshold and gate constants remain private or become advanced API -parameters; the current recommendation is to keep them fixed until broader -validation justifies exposing them. - -`loglik_` can be recomputed from the final interpolated density. Effective -degrees of freedom do not combine trivially across selected and fused experts; -do not silently reuse the bulk value. Either derive the fused influence trace -or return `NaN` for `edf_` until a principled definition is implemented. - -The public API accepts case weights, while the retained experiment is -unweighted. Before enabling the new estimator for weighted fits, define: - -- weighted ranks and tie handling for endpoint bandwidth weights; -- an effective sample size for $k$ and the shrinking gate; -- a weighted order-statistic tail index; -- whether selector confidence adjustments use raw or effective sample size. - -Until those choices are validated, weighted bounded fits should remain on the -legacy path rather than pretending the unweighted selector applies. - -## Tests required - -- Golden PDF vectors against `scripts/bounded_estimator.R` for fixed Uniform, - Beta$(1,2)$, Beta$(0.75,2)$, and Beta$(0.75,0.75)$ samples. -- Explicit samples that select bulk and finite behavior at each endpoint, - including asymmetric lower/upper decisions. -- Nonnegativity, unit mass, monotone CDF, inverse-CDF consistency, and support - truncation. -- Affine-equivariance tests on intervals such as $[-3,7]$. -- Stability with ties, observations exactly at a bound, small samples, and - nearly degenerate samples. -- Regression tests proving that one-sided, unbounded, discrete, - zero-inflated, and weighted fits retain their existing behavior. -- A native rerun of the retained 100-replication validation before making the - new path the default. +The canonical native roadmap now covers the shared one- and two-sided +boundary-expert implementation. See +[`../one-sided-repair/NATIVE_CPP.md`](../one-sided-repair/NATIVE_CPP.md). diff --git a/diagnostic/boundary-repair/README.md b/diagnostic/boundary-repair/README.md index fb263e1..ee49a6c 100644 --- a/diagnostic/boundary-repair/README.md +++ b/diagnostic/boundary-repair/README.md @@ -55,7 +55,7 @@ offset transform, oversmoothed tail expert, or cross-validation selector. - `results/` and `plots/`: corresponding 100-replication outputs. - `RESULTS.md`: final numerical conclusions. - `HANDOFF.md`: concise continuation state. -- `NATIVE_CPP.md`: native C++ implementation plan. +- `NATIVE_CPP.md`: pointer to the shared one- and two-sided native roadmap. Run from the R-package root: diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md new file mode 100644 index 0000000..62c2b53 --- /dev/null +++ b/diagnostic/one-sided-repair/NATIVE_CPP.md @@ -0,0 +1,425 @@ +# Native boundary-expert implementation roadmap + +## Scope + +Implement both selected finite-boundary repairs through one concise internal +path: + +| support | unchanged bulk estimator | candidate endpoints | bandwidth floor | +|---|---|---|---| +| exactly one finite endpoint | power-$3/4$ transform | the finite endpoint | closest 75% of boundary distances | +| two finite endpoints | probit transform | lower and upper, classified independently | all boundary distances | + +The existing transformed estimator remains the bulk component in both cases. +Unbounded continuous, discrete, and zero-inflated behavior remains unchanged. + +The first native version should activate only for unweighted fits with an +automatically selected bandwidth and the default degree two. Weighted fits, +explicit bandwidths, and nondefault degrees retain the current estimator until +their expert semantics have been specified and validated. This is the first +implementation milestone, not the intended final support boundary: experiments +and subsequent activation for weighted and manual-bandwidth fits are important +follow-up work. Keep the bandwidth multiplier supported immediately by +applying it to every expert bandwidth after selection and flooring. + +Do not add a public method switch or another fitted-object representation. + +## Minimal integration point + +Call the repair coordinator only when `type_ == VarType::continuous`, at least +one support bound is finite, `weights` is empty, `bandwidth_spec_` is `NaN`, +and `degree_ == 2`. This makes every initial fallback condition explicit at a +single call site. + +Keep the current body of `Kde1d::fit()` through construction of the normalized +bulk `InterpolationGrid`. Preserve the cleaned observations on their original +scale before applying `boundary_transform()`. Immediately after constructing +the bulk grid: + +1. classify every finite endpoint from original-scale boundary distances; +2. return to the unchanged bulk path if no endpoint is confidently finite; +3. fit a boundary component only for each selected endpoint, using the existing + original-scale grid; +4. form gate probabilities from the normalized bulk CDF; +5. fuse bulk and selected endpoint values and replace `grid_` with the + normalized fused grid. + +The existing PDF, CDF, quantile, simulation, support truncation, and +log-likelihood code then operates on the fused grid. `bandwidth_` continues to +report the bulk bandwidth. + +Boundary distances and local densities can stay in the original units. Every +classifier ratio is dimensionless, and both selected and floor bandwidths +scale with the data, so this is equivalent to the R reference's affine map to +$[0,1]$ without adding a second normalization path. + +No changes should be required in `boundary_transform()`, `boundary_correct()`, +`construct_grid_points()`, `InterpolationGrid`, `PluginBandwidthSelector`, or +the public constructors. + +## Shared private helpers in `kde1d.hpp` + +Keep the implementation in the existing header and add three focused helpers. + +### 1. Endpoint classifier + +Given ascending distances from one endpoint, use +$k=\min(n-1,\lceil2\sqrt n\rceil)$ and + +$$ +\widehat\beta= +\frac{k}{\sum_{i=1}^k +\log\{d_{(k+1)}/\max(d_{(i)},\epsilon d_{(k+1)})\}}}. +$$ + +The scale-relative numerical floor preserves scale equivariance. Select the +finite expert when + +$$ +\widehat\beta\geq0.9, +\qquad +\widehat\beta\left\{1- +\frac{\Phi^{-1}(0.95)}{\sqrt{k}}\right\}\leq1. +$$ + +Run this helper once for the one-sided finite endpoint and independently on +lower and upper distances for two-sided support. Exploding, vanishing, and +ambiguous endpoints all select bulk. A nonpositive $(k+1)$st distance or a +nonfinite/nonpositive logarithmic denominator is a degenerate classifier input +and must also select bulk. + +### 2. Local-polynomial boundary component + +The helper takes boundary distances, ascending evaluation distances, rank +weights, a floor fraction, and degree one or two. + +- Select the weighted bandwidth with `PluginBandwidthSelector`. +- Select the unweighted floor bandwidth from the closest + $\max(4,\lceil q n\rceil)$ distances, where $q=0.75$ for one-sided support + and $q=1$ for two-sided support. +- Use the maximum of the selected and floor bandwidths, then apply the public + multiplier. +- Use rank weights only for bandwidth selection. Evaluate density + contributions with equal observation weights so the estimand remains the + original density. + +Construct the equivalent-kernel coefficients as the first row of the inverse +truncated-normal moment matrix. Generate the moments with + +$$ +\mu_0(a)=\Phi(a),\qquad +\mu_1(a)=-\phi(a),\qquad +\mu_j(a)=(j-1)\mu_{j-2}(a)-a^{j-1}\phi(a). +$$ + +This calculation covers degrees one and two more concisely than separate +determinant formulas. Clamp each component at zero, normalize it on the +distance grid, and average the degree-one and degree-two components. Return +both that density and its diagonal density response for the EDF calculation +described below; the response uses the same clamp mask and normalization as +the density. + +Start with direct $O(nm)$ Gaussian evaluation on the existing grid of +$m\approx401$ points. It follows the retained R references closely and avoids +a second interpolation grid or FFT-specific derivation. Benchmark before +considering an optimized implementation. + +### 3. Boundary-repair coordinator + +This helper owns endpoint distances, average ranks for ties, classification, +local component calls, CDF gates, reflection, and fusion. Use +`tools::get_order()` locally; do not add a general ranking API unless another +production caller needs it. + +For an upper endpoint, compute on ascending reflected distances and reverse the +component once. The floor fraction is the only local-component policy that +differs between one- and two-sided support. + +The helper should return an empty result when every endpoint selects bulk. +`Kde1d::fit()` can then leave the already constructed bulk grid untouched. + +## Gate and fusion + +Let $F_B(x)$ be the bulk CDF and + +$$ +q_n=\min(0.25,n^{-1/2}), +\qquad +s(r)=3r^2-2r^3. +$$ + +For a lower endpoint use + +$$ +w_L(x)=1-s\left(\min\{1,F_B(x)/q_n\}\right), +$$ + +and for an upper endpoint use + +$$ +w_U(x)=1-s\left(\min\{1,(1-F_B(x))/q_n\}\right). +$$ + +Set the gate of every bulk-classified endpoint to zero. The final values are + +$$ +\widehat f(x)= +w_L(x)\widehat f_L(x) ++\{1-w_L(x)-w_U(x)\}\widehat f_B(x) ++w_U(x)\widehat f_U(x). +$$ + +With $q_n\leq0.25$, the endpoint gates do not overlap. The same expression +covers one-sided support by setting the absent endpoint weight to zero. Clamp +the fused values at zero and construct a normalized `InterpolationGrid` on the +existing original-scale grid. + +## Conditional EDF approximation + +The current EDF is already a conditional influence-trace approximation: it +holds the selected bandwidth and final grid normalization fixed. Extend the +same convention to expert selection and fusion rather than returning `NaN`. + +For a degree-$p$ boundary component, let $M_p(a)$ be the truncated-normal +moment matrix above, let $h_p$ be its final bandwidth, let $Z_p$ be the mass +used to normalize its nonnegative density, and let $\widetilde f_p$ denote its +value before clamping and normalization. Its diagonal density response is + +$$ +r_p(x)= +\frac{\mathbf 1\{\widetilde f_p(x)>0\}}{Z_p} +\frac{\phi(0)}{n h_p} +\left[M_p\{d(x)/h_p\}^{-1}\right]_{00}. +$$ + +Only the constant equivalent-kernel coefficient remains because a +self-contribution has kernel argument zero. For the equal linear/quadratic +expert, use + +$$ +f_E(x)=\frac{f_1(x)+f_2(x)}{2}, +\qquad +r_E(x)=\frac{r_1(x)+r_2(x)}{2}. +$$ + +For the bulk component, the existing influence column is its log-density +leverage $\ell_B(x)$, so its diagonal density response is +$r_B(x)=f_B(x)\ell_B(x)$. Fuse the responses with exactly the same gates as the +densities: + +$$ +\begin{aligned} +g(x)&=w_L(x)f_L(x) + +\{1-w_L(x)-w_U(x)\}f_B(x)+w_U(x)f_U(x),\\ +r(x)&=w_L(x)r_L(x) + +\{1-w_L(x)-w_U(x)\}r_B(x)+w_U(x)r_U(x),\\ +\ell(x)&=\frac{r(x)}{g(x)}. +\end{aligned} +$$ + +Thus the mixture leverage is weighted by local density shares, not just by +the gate values. Estimate + +$$ +\operatorname{edf}=\sum_{i=1}^n +\min\{3,\max(0,\ell(X_i))\}, +$$ + +retaining the current per-observation cap. The final common normalization of +$g$ and $r$ cancels in their ratio when its derivative is ignored. + +This approximation conditions on bandwidths, endpoint classifications, CDF +gates, clamp states, and normalization constants. It deliberately omits the +derivatives of those data-adaptive choices. That keeps it consistent with the +existing EDF convention and costs only additional grid-vector arithmetic; no +refits or per-observation matrices are needed. Validate it diagnostically +against the corresponding leave-one-out approximation + +$$ +1+\sum_{i=1}^n +\{\log \widehat f(X_i)-\log \widehat f_{-i}(X_i)\}. +$$ + +First confirm that this diagnostic reproduces the existing bulk EDF to the +expected approximation error. A gate-derivative correction is worth +considering only if the active-expert comparison then shows an additional +systematic discrepancy. + +## Weights and remaining fit metadata + +The experts' rank weights affect bandwidth selection only; density +contributions remain equally weighted, matching the validated estimand. The +first native implementation falls back to bulk when public case weights are +supplied because those weights genuinely change the estimand. Defining +weighted ranks, effective sample size, weighted tail indices, and weighted +confidence adjustments is a separate statistical task. + +Recompute `loglik_` from the final grid using the existing code. Use the +conditional mixture trace above for `edf_` whenever a finite expert is active, +and retain the current calculation unchanged for pure-bulk fits. + +No classifier choice, tail index, boundary bandwidth, or gate state needs to +persist in the fitted object for the first implementation. Diagnostic values +belong in tests and validation scripts rather than the public class layout. + +## Exact production changes + +The intended implementation footprint is: + +1. `include/kde1d/kde1d.hpp` + - preserve original-scale cleaned observations; + - add the three private helpers; + - call the coordinator after bulk-grid construction; + - carry the bulk and expert diagonal responses through fusion for EDF. +2. `test/test.cpp` + - deterministic golden results and fallback behavior. +3. `test/test_numerical_invariants.cpp` + - active-expert normalization, reflection, scale, support, and quantile + invariants. +4. `diagnostic/one-sided-repair/` and `diagnostic/boundary-repair/` + - thin R evaluators and final baseline-versus-native reports. + +Avoid modifying `interpolation.hpp`, `dpik.hpp`, `stats.hpp`, constructors, or +public getters unless implementation evidence shows that it is necessary. + +## Implementation sequence + +1. Synchronize this branch with the isolated PR #34 fix so + `boundary_offset_` is `NaN` before fitting. Record the current production + head and run the native R evaluators once to create one- and two-sided + baseline outputs before changing estimator behavior. +2. Add the eligibility check and preserve original-scale observations. With + the coordinator returning bulk, verify tight numerical parity for every + existing support type. +3. Implement the shared endpoint classifier and deterministic finite/bulk + tests for lower and upper endpoints. +4. Implement the shared degree-one/two equivalent-kernel evaluator. Validate + both bandwidth-floor policies against the retained R references. +5. Activate one-sided fusion with the 75% floor and verify the selected + one-sided scenarios. +6. Activate two-sided fusion with the full-sample floor and verify independent + lower/upper decisions, including asymmetric densities. +7. Complete log-likelihood and conditional-EDF handling, numerical regression + tests, and fit-time benchmarks. +8. Run the larger R validation against the recorded native baselines, retain + only final comparison artifacts, and prepare the PR report. + +Each step should be a separately testable commit. Avoid refactoring unrelated +fit logic while implementing the method. + +## Important follow-up: weights and manual bandwidths + +Do not close the estimator work after the initial unweighted, automatic- +bandwidth activation. Keep the following experiments and production activation +as explicit roadmap items, preferably in follow-up commits or a follow-up PR so +the initial implementation remains reviewable. + +### Public case weights + +Public case weights change the target density, unlike the endpoint-targeting +weights used only to select expert bandwidths. A weighted expert should +therefore use public case weights for density contributions and use the product +of public and endpoint-targeting weights for bandwidth selection. Before +activation, compare and validate choices for: + +- weighted average ranks and endpoint distances; +- effective sample size in $k$, $q_n$, and the classifier confidence term; +- a weighted order-statistic tail index; +- defining the closest 75% floor by cumulative public weight rather than row + count; +- weighted diagonal responses and EDF validation. + +Experiments should include highly unequal weights, weights concentrated near +and far from the boundary, zero weights, global rescaling of all weights, and +integer weights compared with explicitly replicated observations. Require +weight-scale invariance, approximate replication equivalence, stable endpoint +classification, and acceptable global/boundary ISE before removing the +weighted fallback. + +### Manually specified bandwidths + +A manual bulk bandwidth is expressed on the transformed scale, whereas local +boundary bandwidths are expressed in original data units. Reusing the same +number for both is therefore invalid. The leading candidate is to compute the +automatic bulk reference bandwidth $h_{B,0}$ and interpret the manual choice +$h_B$ through the dimensionless ratio + +$$ +\rho=\frac{h_B}{h_{B,0}}, +$$ + +then multiply every automatically selected and floored expert bandwidth by +$\rho$. This preserves the requested bulk bandwidth while treating it as a +global smoothing adjustment. Compare this with leaving expert bandwidths +automatic when only the bulk bandwidth is manual; reject direct numerical +reuse across scales. + +Run the comparison over manual-to-automatic ratios such as $0.5$, $0.75$, $1$, +$1.5$, and $2$, several support rescalings, both support types, finite and +exploding endpoint shapes, and representative visual fits. Include the extra +cost of computing $h_{B,0}$ in the manual case. Activate manual-bandwidth fits +only after selecting and documenting one interpretation that preserves affine +equivariance and behaves predictably with `multiplier_`. + +Finally test weighted and manual bandwidths together after each has been +validated separately. Nondefault local-likelihood degrees remain a lower- +priority extension because the selected boundary expert deliberately averages +degrees one and two. + +## Native tests + +Add compact tests to the existing executables. + +Shared coverage: + +- nonnegativity, unit mass, monotone CDF, quantile round trips, finite + log-likelihood and EDF, and support truncation; +- exact EDF parity with the current path when no expert is active, plus + diagnostic comparison with leave-one-out log-likelihood optimism when an + expert is active; +- scaling over several orders of magnitude; +- ties, observations exactly at an endpoint, small samples, and nearly + degenerate samples; +- regression coverage proving that unbounded, discrete, zero-inflated, + weighted, fixed-bandwidth, and nondefault-degree fits retain the current + path; +- fit-time benchmarks at representative $n$ values. + +One-sided coverage: + +- deterministic Exponential, half-normal, Gamma$(2)$, Gamma$(0.75)$, and + Lomax samples; +- lower/upper reflection while the expert is active; +- finite and bulk classifier outcomes; +- golden grid or PDF values against `one_sided_estimator.R`. + +Two-sided coverage: + +- deterministic Uniform, Beta$(1,2)$, Beta$(0.75,2)$, and + Beta$(0.75,0.75)$ samples; +- lower and upper finite/bulk outcomes, including asymmetric decisions; +- affine equivariance on non-unit intervals; +- golden grid or PDF values against `bounded_estimator.R`. + +If direct local evaluation is materially expensive, optimize only after a +profile identifies it as the relevant fit cost. + +## R validation without C++ experiment bloat + +Keep Monte Carlo comparisons in R. Use small native-evaluator scripts that run +the installed estimator for deterministic scenario seeds and write +replication-level global and boundary ISE plus aggregate squared bias and +variance. Run them once at the recorded baseline commit and once at the +candidate commit, then join the outputs in reporting scripts. + +This avoids a legacy-mode switch in the public C++ API and avoids maintaining +two production estimator paths solely for benchmarking. + +The final one-sided suite should expand the retained scenarios with +intermediate sample sizes, steeper finite-endpoint slopes, heavier remote +tails, upper-bounded reflections, and visual realizations. The final two-sided +suite should retain varied symmetric and asymmetric finite, vanishing, and +exploding endpoint shapes plus local boundary plots. Report paired ISE ratios +with Monte Carlo uncertainty, global and local bias/variance, classifier rates +computed by matching R code, visual examples, and fit time relative to the +current transformed baselines. diff --git a/diagnostic/one-sided-repair/README.md b/diagnostic/one-sided-repair/README.md index 66f7a1d..1fa174d 100644 --- a/diagnostic/one-sided-repair/README.md +++ b/diagnostic/one-sided-repair/README.md @@ -35,6 +35,7 @@ have been removed. `plots/local-floor-fraction-ablation.pdf`: current tuning evidence. - `RESULTS.md`: numerical conclusions. - `HANDOFF.md`: implementation state and next steps. +- `NATIVE_CPP.md`: shared one- and two-sided native implementation roadmap. Run from the R-package root: From bacade544290a52d574941a74e34e10d6954e961 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 15:00:12 +0200 Subject: [PATCH 05/25] Implement one-sided boundary expert --- diagnostic/one-sided-repair/NATIVE_CPP.md | 13 +- include/kde1d/kde1d.hpp | 268 +++++++++++++++++++++- test/test.cpp | 48 ++++ 3 files changed, 320 insertions(+), 9 deletions(-) diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md index 62c2b53..1983ec9 100644 --- a/diagnostic/one-sided-repair/NATIVE_CPP.md +++ b/diagnostic/one-sided-repair/NATIVE_CPP.md @@ -13,9 +13,10 @@ path: The existing transformed estimator remains the bulk component in both cases. Unbounded continuous, discrete, and zero-inflated behavior remains unchanged. -The first native version should activate only for unweighted fits with an -automatically selected bandwidth and the default degree two. Weighted fits, -explicit bandwidths, and nondefault degrees retain the current estimator until +The first native version should activate only for samples of at least 16 +observations, unweighted or constant-weight fits, an automatically selected +bandwidth, and the default degree two. Nonconstant weighted fits, explicit +bandwidths, and nondefault degrees retain the current estimator until their expert semantics have been specified and validated. This is the first implementation milestone, not the intended final support boundary: experiments and subsequent activation for weighted and manual-bandwidth fits are important @@ -27,9 +28,9 @@ Do not add a public method switch or another fitted-object representation. ## Minimal integration point Call the repair coordinator only when `type_ == VarType::continuous`, at least -one support bound is finite, `weights` is empty, `bandwidth_spec_` is `NaN`, -and `degree_ == 2`. This makes every initial fallback condition explicit at a -single call site. +one support bound is finite, at least 16 cleaned observations remain, case +weights are absent or constant, `bandwidth_spec_` is `NaN`, and `degree_ == 2`. +This makes every initial fallback condition explicit at a single call site. Keep the current body of `Kde1d::fit()` through construction of the normalized bulk `InterpolationGrid`. Preserve the cleaned observations on their original diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 1f5c750..f83b864 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -121,6 +121,12 @@ class Kde1d void set_interpolation_grid(const interp::InterpolationGrid& grid); private: + struct BoundaryComponent + { + Eigen::VectorXd density; + Eigen::VectorXd response; + }; + // data members interp::InterpolationGrid grid_; double xmin_; @@ -185,6 +191,16 @@ class Kde1d double multiplier, size_t degree, const Eigen::VectorXd& weights) const; + bool is_finite_endpoint(Eigen::VectorXd distances) const; + BoundaryComponent fit_boundary_component( + const Eigen::VectorXd& distances, + const Eigen::VectorXd& evaluation_distances, + const Eigen::VectorXd& bandwidth_weights, + double floor_fraction, + size_t degree) const; + void repair_boundaries(const Eigen::VectorXd& observations, + const Eigen::VectorXd& grid_points, + Eigen::VectorXd& influences); std::string as_str(VarType type) const; VarType as_enum(std::string type) const; @@ -329,6 +345,17 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) Eigen::VectorXd w = weights; tools::remove_nans(xx, w); + // Nonconstant case weights and manual bandwidths need separate expert + // semantics; constant weights are equivalent to an unweighted sample. + const bool unweighted = w.size() == 0 || w.minCoeff() == w.maxCoeff(); + const bool repair_one_sided = type_ == VarType::continuous && + xx.size() >= 16 && unweighted && + std::isnan(bandwidth_spec_) && degree_ == 2 && + (std::isnan(xmin_) != std::isnan(xmax_)); + Eigen::VectorXd boundary_observations; + if (repair_one_sided) + boundary_observations = xx; + if (w.size() > 0) { w /= w.mean(); } @@ -392,9 +419,15 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) // order grid points from left to right grid_points = finalize_grid(grid_points); + Eigen::VectorXd influences = fitted.col(1); + if (std::isnan(xmin_) && !std::isnan(xmax_)) + influences.reverseInPlace(); + // construct interpolation grid // (3 iterations for normalization to a proper density) grid_ = interp::InterpolationGrid(grid_points, values, 3); + if (repair_one_sided) + repair_boundaries(boundary_observations, grid_points, influences); // calculate log-likelihood of final estimate xx = boundary_transform(xx, true); @@ -415,9 +448,7 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) } // calculate effective degrees of freedom - Eigen::VectorXd influences = fitted.col(1).cwiseMin(3.0).cwiseMax(0); - if (std::isnan(xmin_) && !std::isnan(xmax_)) - influences.reverseInPlace(); + influences = influences.cwiseMin(3.0).cwiseMax(0); interp::InterpolationGrid infl_grid(grid_points, influences, 0); influences = infl_grid.interpolate(xx).array(); edf_ = influences.sum() + static_cast(prob0_ > 0); @@ -917,6 +948,237 @@ Kde1d::finalize_grid(Eigen::VectorXd& grid_points) return grid_points; } +//! Classifies a support endpoint from the power law of its closest order +//! statistics. Ambiguous and numerically degenerate cases retain the bulk fit. +inline bool +Kde1d::is_finite_endpoint(Eigen::VectorXd distances) const +{ + std::sort(distances.data(), distances.data() + distances.size()); + const size_t tail_count = + std::min(static_cast(distances.size() - 1), + static_cast(std::ceil(2.0 * std::sqrt(distances.size())))); + const double threshold = distances(tail_count); + if (!(threshold > 0.0) || !std::isfinite(threshold)) + return false; + + double log_sum = 0.0; + const double distance_floor = + std::numeric_limits::epsilon() * threshold; + for (size_t index = 0; index < tail_count; ++index) { + log_sum += std::log(threshold / std::max(distances(index), distance_floor)); + } + if (!(log_sum > 0.0) || !std::isfinite(log_sum)) + return false; + + const double tail_index = static_cast(tail_count) / log_sum; + // 1.64485 is the 95% standard-normal quantile used by the R selector. + return tail_index >= 0.9 && + tail_index * (1.0 - 1.6448536269514722 / std::sqrt(tail_count)) <= 1.0; +} + +//! Fits one Gaussian local-polynomial endpoint component. Targeting weights +//! select its bandwidth only; equal observation contributions preserve the +//! original density estimand. +inline Kde1d::BoundaryComponent +Kde1d::fit_boundary_component(const Eigen::VectorXd& distances, + const Eigen::VectorXd& evaluation_distances, + const Eigen::VectorXd& bandwidth_weights, + double floor_fraction, + size_t degree) const +{ + bandwidth::PluginBandwidthSelector selector(distances, bandwidth_weights); + double bandwidth = selector.select_bandwidth(degree); + + Eigen::VectorXd ordered_distances = distances; + std::sort(ordered_distances.data(), + ordered_distances.data() + ordered_distances.size()); + const Eigen::Index floor_count = std::min( + distances.size(), + std::max( + 4, + static_cast(std::ceil(floor_fraction * distances.size())))); + bandwidth::PluginBandwidthSelector floor_selector( + ordered_distances.head(floor_count)); + bandwidth = + std::max(bandwidth, floor_selector.select_bandwidth(degree)) * multiplier_; + if (!(bandwidth > 0.0) || !std::isfinite(bandwidth)) + return {}; + + BoundaryComponent component{ Eigen::VectorXd(evaluation_distances.size()), + Eigen::VectorXd(evaluation_distances.size()) }; + for (Eigen::Index row = 0; row < evaluation_distances.size(); ++row) { + const double boundary_position = evaluation_distances(row) / bandwidth; + const double normal_density = + K0_ * std::exp(-0.5 * boundary_position * boundary_position); + Eigen::VectorXd moments(2 * degree + 1); + moments(0) = + stats::pnorm(Eigen::VectorXd::Constant(1, boundary_position))(0); + moments(1) = -normal_density; + for (size_t order = 2; order < static_cast(moments.size()); + ++order) { + moments(order) = (order - 1.0) * moments(order - 2) - + std::pow(boundary_position, order - 1) * normal_density; + } + + Eigen::MatrixXd moment_matrix(degree + 1, degree + 1); + for (size_t column = 0; column <= degree; ++column) { + for (size_t matrix_row = 0; matrix_row <= degree; ++matrix_row) + moment_matrix(matrix_row, column) = moments(matrix_row + column); + } + const Eigen::VectorXd coefficients = moment_matrix.inverse().row(0); + + double density = 0.0; + for (Eigen::Index observation = 0; observation < distances.size(); + ++observation) { + const double kernel_argument = + (evaluation_distances(row) - distances(observation)) / bandwidth; + double polynomial = coefficients(degree); + for (size_t order = degree; order > 0; --order) + polynomial = polynomial * kernel_argument + coefficients(order - 1); + density += + K0_ * std::exp(-0.5 * kernel_argument * kernel_argument) * polynomial; + } + component.density(row) = + density / (static_cast(distances.size()) * bandwidth); + component.response(row) = + K0_ * coefficients(0) / + (static_cast(distances.size()) * bandwidth); + } + + for (Eigen::Index row = 0; row < component.density.size(); ++row) { + if (!(component.density(row) > 0.0) || + !std::isfinite(component.density(row)) || + !std::isfinite(component.response(row))) { + component.density(row) = 0.0; + component.response(row) = 0.0; + } + } + double mass = 0.0; + for (Eigen::Index row = 0; row < component.density.size() - 1; ++row) { + mass += (evaluation_distances(row + 1) - evaluation_distances(row)) * + (component.density(row) + component.density(row + 1)) / 2.0; + } + if (!(mass > 0.0) || !std::isfinite(mass)) + return {}; + component.density /= mass; + component.response /= mass; + return component; +} + +//! Replaces the transformed bulk density near confidently finite endpoints +//! and carries the same local mixture through the diagonal EDF response. +inline void +Kde1d::repair_boundaries(const Eigen::VectorXd& observations, + const Eigen::VectorXd& grid_points, + Eigen::VectorXd& influences) +{ + Eigen::VectorXd lower_distances; + Eigen::VectorXd upper_distances; + bool repair_lower = !std::isnan(xmin_); + bool repair_upper = !std::isnan(xmax_); + if (repair_lower) { + lower_distances = observations.array() - xmin_; + repair_lower = is_finite_endpoint(lower_distances); + } + if (repair_upper) { + upper_distances = xmax_ - observations.array(); + repair_upper = is_finite_endpoint(upper_distances); + } + if (!repair_lower && !repair_upper) + return; + + const double boundary_fraction = + std::min(0.25, 1.0 / std::sqrt(observations.size())); + auto endpoint_weight = [&](double probability) { + const double position = std::min(1.0, probability / boundary_fraction); + return 1.0 - + (3.0 * position * position - 2.0 * position * position * position); + }; + auto targeting_weights = [&](const Eigen::VectorXd& distances) { + Eigen::VectorXd weights(distances.size()); + const Eigen::VectorXi order = tools::get_order(distances); + Eigen::Index first = 0; + while (first < order.size()) { + Eigen::Index last = first; + while (last + 1 < order.size() && + distances(order(last + 1)) == distances(order(first))) + ++last; + const double probability = static_cast(first + last + 1) / + (2.0 * static_cast(distances.size())); + for (Eigen::Index index = first; index <= last; ++index) + weights(order(index)) = endpoint_weight(probability); + first = last + 1; + } + return weights; + }; + + const double floor_fraction = + (!std::isnan(xmin_) && !std::isnan(xmax_)) ? 1.0 : 0.75; + auto fit_endpoint = [&](const Eigen::VectorXd& distances, + const Eigen::VectorXd& evaluation_distances) { + const Eigen::VectorXd weights = targeting_weights(distances); + BoundaryComponent linear = fit_boundary_component( + distances, evaluation_distances, weights, floor_fraction, 1); + BoundaryComponent quadratic = fit_boundary_component( + distances, evaluation_distances, weights, floor_fraction, 2); + if (linear.density.size() == 0 || quadratic.density.size() == 0) + return BoundaryComponent{}; + linear.density = (linear.density + quadratic.density) / 2.0; + linear.response = (linear.response + quadratic.response) / 2.0; + return linear; + }; + + BoundaryComponent lower; + BoundaryComponent upper; + if (repair_lower) { + lower = fit_endpoint(lower_distances, grid_points.array() - xmin_); + repair_lower = lower.density.size() > 0; + } + if (repair_upper) { + Eigen::VectorXd evaluation_distances = + (xmax_ - grid_points.array()).reverse(); + upper = fit_endpoint(upper_distances, evaluation_distances); + repair_upper = upper.density.size() > 0; + if (repair_upper) { + upper.density.reverseInPlace(); + upper.response.reverseInPlace(); + } + } + if (!repair_lower && !repair_upper) + return; + + const Eigen::VectorXd bulk_density = grid_.get_values(); + const Eigen::VectorXd probabilities = grid_.integrate(grid_points, true); + Eigen::VectorXd lower_weights = Eigen::VectorXd::Zero(grid_points.size()); + Eigen::VectorXd upper_weights = Eigen::VectorXd::Zero(grid_points.size()); + for (Eigen::Index row = 0; row < grid_points.size(); ++row) { + if (repair_lower) { + lower_weights(row) = endpoint_weight(probabilities(row)); + } + if (repair_upper) { + upper_weights(row) = endpoint_weight(1.0 - probabilities(row)); + } + } + + Eigen::VectorXd density(grid_points.size()); + Eigen::VectorXd response(grid_points.size()); + for (Eigen::Index row = 0; row < grid_points.size(); ++row) { + const double bulk_weight = 1.0 - lower_weights(row) - upper_weights(row); + density(row) = bulk_weight * bulk_density(row); + response(row) = bulk_weight * bulk_density(row) * influences(row); + if (repair_lower) { + density(row) += lower_weights(row) * lower.density(row); + response(row) += lower_weights(row) * lower.response(row); + } + if (repair_upper) { + density(row) += upper_weights(row) * upper.density(row); + response(row) += upper_weights(row) * upper.response(row); + } + influences(row) = density(row) > 0.0 ? response(row) / density(row) : 0.0; + } + grid_ = interp::InterpolationGrid(grid_points, density.cwiseMax(0.0), 3); +} + // Bandwidth for Kernel Density Estimation //' @param x vector of observations //' @param bandwidth bandwidth parameter, NA for automatic selection. diff --git a/test/test.cpp b/test/test.cpp index a3c76e2..5e426e7 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -133,6 +133,54 @@ TEST_CASE("one-boundary fits are reflection equivariant", "[boundary-reflection] CHECK(left_bounded.get_edf() == Approx(right_bounded.get_edf())); } +TEST_CASE("one-sided finite endpoints use the boundary expert", + "[boundary-expert]") +{ + const Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + const Eigen::VectorXd observations = (-(1.0 - probabilities.array()).log()); + Kde1d fit(0.0, NAN, "continuous"); + fit.fit(observations); + + // A manual fit with the selected bulk bandwidth bypasses boundary repair. + Kde1d bulk(0.0, NAN, "continuous", 1.0, fit.get_bandwidth()); + bulk.fit(observations); + CHECK((fit.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > 0.01); + + Eigen::VectorXd expected_density(6); + expected_density << 0.9905722, 0.9905911, 0.9885084, 0.9473293, 0.7314338, + 0.0077356; + Eigen::VectorXd selected_density(6); + selected_density << fit.get_values()(0), fit.get_values()(4), + fit.get_values()(24), fit.get_values()(49), fit.get_values()(99), + fit.get_values()(199); + CHECK(selected_density.isApprox(expected_density, 2e-4)); + CHECK(std::isfinite(fit.get_edf())); + + Kde1d reflected(NAN, 0.0, "continuous"); + reflected.fit(-observations); + CHECK(fit.get_grid_points().isApprox(-reflected.get_grid_points().reverse(), + 1e-12)); + CHECK(fit.get_values().isApprox(reflected.get_values().reverse(), 1e-12)); + CHECK(fit.get_edf() == Approx(reflected.get_edf()).epsilon(1e-12)); +} + +TEST_CASE("one-sided vanishing endpoints retain the bulk fit", + "[boundary-expert]") +{ + const Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + const Eigen::VectorXd observations = probabilities.array().sqrt(); + Kde1d fit(0.0, NAN, "continuous"); + fit.fit(observations); + + Kde1d bulk(0.0, NAN, "continuous", 1.0, fit.get_bandwidth()); + bulk.fit(observations); + CHECK(fit.get_grid_points().isApprox(bulk.get_grid_points(), 1e-12)); + CHECK(fit.get_values().isApprox(bulk.get_values(), 1e-12)); + CHECK(fit.get_edf() == Approx(bulk.get_edf()).epsilon(1e-12)); +} + TEST_CASE("finite support truncates density", "[finite-support]") { Eigen::VectorXd observations = Eigen::VectorXd::LinSpaced(200, 0.0, 1.0); From e6e7e00c855ff9441e8b2d80150d70e9f5dd8625 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 15:03:14 +0200 Subject: [PATCH 06/25] Activate two-sided boundary experts --- include/kde1d/kde1d.hpp | 12 +++---- test/test.cpp | 72 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 78 insertions(+), 6 deletions(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index f83b864..823c7b3 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -348,12 +348,12 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) // Nonconstant case weights and manual bandwidths need separate expert // semantics; constant weights are equivalent to an unweighted sample. const bool unweighted = w.size() == 0 || w.minCoeff() == w.maxCoeff(); - const bool repair_one_sided = type_ == VarType::continuous && - xx.size() >= 16 && unweighted && - std::isnan(bandwidth_spec_) && degree_ == 2 && - (std::isnan(xmin_) != std::isnan(xmax_)); + const bool use_boundary_repair = + type_ == VarType::continuous && xx.size() >= 16 && unweighted && + std::isnan(bandwidth_spec_) && degree_ == 2 && + (!std::isnan(xmin_) || !std::isnan(xmax_)); Eigen::VectorXd boundary_observations; - if (repair_one_sided) + if (use_boundary_repair) boundary_observations = xx; if (w.size() > 0) { @@ -426,7 +426,7 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) // construct interpolation grid // (3 iterations for normalization to a proper density) grid_ = interp::InterpolationGrid(grid_points, values, 3); - if (repair_one_sided) + if (use_boundary_repair) repair_boundaries(boundary_observations, grid_points, influences); // calculate log-likelihood of final estimate diff --git a/test/test.cpp b/test/test.cpp index 5e426e7..75acbb8 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -181,6 +181,78 @@ TEST_CASE("one-sided vanishing endpoints retain the bulk fit", CHECK(fit.get_edf() == Approx(bulk.get_edf()).epsilon(1e-12)); } +TEST_CASE("two-sided finite endpoints use the boundary experts", + "[boundary-expert]") +{ + const Eigen::VectorXd observations = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + Kde1d fit(0.0, 1.0, "continuous"); + fit.fit(observations); + + Kde1d bulk(0.0, 1.0, "continuous", 1.0, fit.get_bandwidth()); + bulk.fit(observations); + CHECK((fit.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > 0.01); + + Eigen::VectorXd expected_density(6); + expected_density << 1.0368661, 1.0367788, 1.0250191, 0.9972352, 1.0231640, + 1.0368661; + Eigen::VectorXd selected_density(6); + selected_density << fit.get_values()(0), fit.get_values()(49), + fit.get_values()(99), fit.get_values()(199), fit.get_values()(299), + fit.get_values()(400); + CHECK(selected_density.isApprox(expected_density, 2e-4)); + CHECK(std::isfinite(fit.get_edf())); + + Kde1d scaled(-3.0, 7.0, "continuous"); + scaled.fit(-3.0 + 10.0 * observations.array()); + CHECK(((scaled.get_grid_points().array() + 3.0) / 10.0) + .matrix() + .isApprox(fit.get_grid_points(), 1e-12)); + CHECK((10.0 * scaled.get_values()).isApprox(fit.get_values(), 1e-10)); + CHECK(scaled.get_edf() == Approx(fit.get_edf()).epsilon(1e-10)); +} + +TEST_CASE("two-sided endpoints are classified independently", + "[boundary-expert]") +{ + const Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + const Eigen::VectorXd observations = + 1.0 - (1.0 - probabilities.array()).sqrt(); + Kde1d fit(0.0, 1.0, "continuous"); + fit.fit(observations); + + Eigen::VectorXd expected_density(6); + expected_density << 1.9952890, 1.9913280, 1.9839701, 0.9946680, 0.0562144, + 0.0000020; + Eigen::VectorXd selected_density(6); + selected_density << fit.get_values()(0), fit.get_values()(49), + fit.get_values()(99), fit.get_values()(199), fit.get_values()(299), + fit.get_values()(400); + CHECK(selected_density.isApprox(expected_density, 2e-4)); + + Kde1d reflected(0.0, 1.0, "continuous"); + reflected.fit(1.0 - observations.array()); + CHECK(fit.get_values().isApprox(reflected.get_values().reverse(), 1e-12)); + CHECK(fit.get_edf() == Approx(reflected.get_edf()).epsilon(1e-12)); +} + +TEST_CASE("two-sided exploding endpoints retain the bulk fit", + "[boundary-expert]") +{ + const Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + const Eigen::VectorXd observations = + (0.5 * std::acos(-1.0) * probabilities.array()).sin().square(); + Kde1d fit(0.0, 1.0, "continuous"); + fit.fit(observations); + + Kde1d bulk(0.0, 1.0, "continuous", 1.0, fit.get_bandwidth()); + bulk.fit(observations); + CHECK(fit.get_values().isApprox(bulk.get_values(), 1e-12)); + CHECK(fit.get_edf() == Approx(bulk.get_edf()).epsilon(1e-12)); +} + TEST_CASE("finite support truncates density", "[finite-support]") { Eigen::VectorXd observations = Eigen::VectorXd::LinSpaced(200, 0.0, 1.0); From df1b0623c6c7653431911574f414a29d4dc89417 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 15:15:54 +0200 Subject: [PATCH 07/25] Validate native boundary experts --- benchmark/benchmark.cpp | 17 ++ diagnostic/NATIVE_RESULTS.md | 79 ++++++++ diagnostic/README.md | 4 + diagnostic/validate_native_boundary_experts.R | 184 ++++++++++++++++++ 4 files changed, 284 insertions(+) create mode 100644 diagnostic/NATIVE_RESULTS.md create mode 100644 diagnostic/validate_native_boundary_experts.R diff --git a/benchmark/benchmark.cpp b/benchmark/benchmark.cpp index 281983d..a1251b4 100644 --- a/benchmark/benchmark.cpp +++ b/benchmark/benchmark.cpp @@ -10,6 +10,9 @@ TEST_CASE("continuous KDE performance", "[!benchmark]") unbounded.array() += 0.35 * (4.0 * unbounded.array()).sin(); Eigen::VectorXd bounded = (1.0 / (1.0 + (-unbounded.array()).exp())).matrix(); + Eigen::VectorXd probabilities = Eigen::VectorXd::LinSpaced( + unbounded.size(), 0.5 / unbounded.size(), 1.0 - 0.5 / unbounded.size()); + Eigen::VectorXd one_sided = (-(1.0 - probabilities.array()).log()); Eigen::VectorXd weights = Eigen::VectorXd::LinSpaced(10000, 0.5, 1.5); BENCHMARK("fit/end-to-end/bounded/tll/n=10000") @@ -19,6 +22,20 @@ TEST_CASE("continuous KDE performance", "[!benchmark]") return fit.get_loglik(); }; + BENCHMARK("fit/end-to-end/one-sided-finite-expert/tll/n=10000") + { + kde1d::Kde1d fit(0.0, NAN, "continuous", 1.0, NAN, 2, 400); + fit.fit(one_sided); + return fit.get_loglik(); + }; + + BENCHMARK("fit/end-to-end/two-sided-finite-experts/tll/n=10000") + { + kde1d::Kde1d fit(0.0, 1.0, "continuous", 1.0, NAN, 2, 400); + fit.fit(probabilities); + return fit.get_loglik(); + }; + BENCHMARK("fit/fixed-bandwidth/unbounded/tll/n=10000") { kde1d::Kde1d fit(NAN, NAN, "continuous", 1.0, 0.3, 2, 400); diff --git a/diagnostic/NATIVE_RESULTS.md b/diagnostic/NATIVE_RESULTS.md new file mode 100644 index 0000000..8067ea6 --- /dev/null +++ b/diagnostic/NATIVE_RESULTS.md @@ -0,0 +1,79 @@ +# Native boundary-expert validation + +## Statistical validation + +The native candidate was compared with commit `4f3d148`, immediately before +the expert implementation. The paired experiment used 100 replications at +$n=25,100,1000,2000$. One-sided scenarios were Exponential, half-normal, +Gamma$(2)$, Gamma$(0.75)$, and Lomax$(2)$; two-sided scenarios were Uniform and +six symmetric or asymmetric beta densities. Ratios below average the +scenario-specific ratios of mean ISE. Parentheses contain paired Monte Carlo +standard errors. + +| support | $n$ | global ISE ratio | boundary ISE ratio | +|---|---:|---:|---:| +| one-sided | 25 | 0.932 (0.008) | 0.896 (0.016) | +| one-sided | 100 | 0.929 (0.009) | 0.903 (0.016) | +| one-sided | 1000 | 0.907 (0.012) | 0.857 (0.017) | +| one-sided | 2000 | 0.881 (0.015) | 0.824 (0.020) | +| two-sided | 25 | 0.874 (0.021) | 0.862 (0.020) | +| two-sided | 100 | 0.911 (0.008) | 0.917 (0.007) | +| two-sided | 1000 | 0.939 (0.007) | 0.954 (0.006) | +| two-sided | 2000 | 0.944 (0.007) | 0.955 (0.006) | + +Average integrated variance ratios range from 0.93 to 0.94 one-sided and from +0.87 to 0.96 two-sided. Boundary variance ratios range from 0.88 to 0.90 and +from 0.86 to 0.97, respectively. The extra small-sample bias is the intended +price for smoother boundary realizations; at $n=1000,2000$, average integrated +squared bias is also lower than baseline. + +The main accepted losses remain the difficult shapes identified by the R +experiments. At $n=2000$, Gamma$(0.75)$ has global/boundary ratios +1.085/1.098, Beta$(0.75,2)$ has 1.075/1.072, and the reflected +Beta$(2,0.75)$ has 1.027/1.026. Gamma$(2)$ and Beta$(2,2)$ select bulk in every +large-sample replication and are exactly unchanged. Uniform, Beta$(1,2)$, and +Beta$(2,1)$ have $n=2000$ global ratios 0.844, 0.817, and 0.830. + +The deterministic native tests agree with the retained R reference values to +within $2\times10^{-4}$ relative tolerance and cover lower/upper reflection, +independent two-sided endpoint decisions, exploding/vanishing fallback, and +affine support changes. + +## EDF check + +The conditional mixture EDF was compared with + +$$ +1+\sum_i\{\log\widehat f(X_i)-\log\widehat f_{-i}(X_i)\}. +$$ + +For deterministic finite-endpoint samples at $n=25,50,100$, the discrepancy +was 0.08--0.30 EDF units for Uniform and Exponential examples. The asymmetric +Beta$(1,2)$ discrepancy was 0.27--0.33 at $n=50,100$ and 0.84 at $n=25$. +This is adequate for the existing asymptotic EDF convention and does not +justify a gate-derivative correction. Pure-bulk fits retain the old EDF +exactly. + +## Fit time + +Release builds were timed against `4f3d148`. Bulk-classified fits incur only +sorting and remained within about 3% of baseline for $n=100$--$2000$. Active +experts cost more because the concise implementation directly evaluates the +Gaussian kernels on the 401-point grid: + +| active endpoints | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:| +| one | 1.70 ms (4.4x) | 5.93 ms (12.4x) | 10.67 ms (18.5x) | +| two | 2.90 ms (7.5x) | 10.41 ms (23.5x) | 18.84 ms (36.7x) | + +The absolute cost remains below 20 ms at $n=2000$. Keep the direct evaluator +for the first PR; optimize only if downstream profiling shows fit time is +material. + +## Reproduction + +Install the package with a clean native rebuild at each revision and run +`validate_native_boundary_experts.R`, giving each run a distinct method label +and output file. The script writes replication-level ISE/EDF/log-likelihood and +a companion bias/variance summary. Join the two raw files by support, +scenario, sample size, and replication for paired ratios and uncertainty. diff --git a/diagnostic/README.md b/diagnostic/README.md index 9624814..85687d3 100644 --- a/diagnostic/README.md +++ b/diagnostic/README.md @@ -36,3 +36,7 @@ results, and its current recommendations live in The follow-up for supports with exactly one finite endpoint lives in [`one-sided-repair/`](one-sided-repair/README.md). + +The shared native implementation is evaluated by +[`validate_native_boundary_experts.R`](validate_native_boundary_experts.R), +with current results summarized in [`NATIVE_RESULTS.md`](NATIVE_RESULTS.md). diff --git a/diagnostic/validate_native_boundary_experts.R b/diagnostic/validate_native_boundary_experts.R new file mode 100644 index 0000000..2a0a79f --- /dev/null +++ b/diagnostic/validate_native_boundary_experts.R @@ -0,0 +1,184 @@ +# Evaluate one native kde1d revision. Run once at the baseline commit and once +# at the candidate commit, then compare rows by scenario, size, and replication. + +arguments <- commandArgs(trailingOnly = TRUE) +if (length(arguments) < 2L || length(arguments) > 4L) { + stop("usage: script method output.csv [replications] [library-path]") +} +if (length(arguments) == 4L) { + .libPaths(c(arguments[[4L]], .libPaths())) +} +library(kde1d) + +method <- arguments[[1L]] +output_file <- arguments[[2L]] +replications <- if (length(arguments) >= 3L) { + as.integer(arguments[[3L]]) +} else { + 100L +} +if (!is.finite(replications) || replications < 2L) { + stop("replications must be at least two") +} + +integrate_values <- function(points, values) { + sum(diff(points) * (values[-length(values)] + values[-1L]) / 2) +} + +one_sided <- list( + exponential = list( + random = function(n) rexp(n), + density = dexp, + quantile = qexp + ), + half_normal = list( + random = function(n) abs(rnorm(n)), + density = function(x) 2 * dnorm(x), + quantile = function(p) qnorm((p + 1) / 2) + ), + gamma_2 = list( + random = function(n) rgamma(n, 2), + density = function(x) dgamma(x, 2), + quantile = function(p) qgamma(p, 2) + ), + gamma_075 = list( + random = function(n) rgamma(n, 0.75), + density = function(x) dgamma(x, 0.75), + quantile = function(p) qgamma(p, 0.75) + ), + lomax_2 = list( + random = function(n) (1 - runif(n))^(-0.5) - 1, + density = function(x) 2 / (1 + x)^3, + quantile = function(p) (1 - p)^(-0.5) - 1 + ) +) +two_sided <- list( + uniform = c(1, 1), + beta_1_2 = c(1, 2), + beta_2_1 = c(2, 1), + beta_075_2 = c(0.75, 2), + beta_2_075 = c(2, 0.75), + beta_075_075 = c(0.75, 0.75), + beta_2_2 = c(2, 2) +) +sample_sizes <- c(25L, 100L, 1000L, 2000L) +result_rows <- list() +summary_rows <- list() + +summarize_estimates <- function(points, estimates, truth, boundary) { + mean_density <- rowMeans(estimates) + c( + global_squared_bias = integrate_values( + points, (mean_density - truth)^2 + ), + global_variance = integrate_values( + points, rowMeans((estimates - mean_density)^2) + ), + boundary_squared_bias = integrate_values( + points[boundary], (mean_density[boundary] - truth[boundary])^2 + ), + boundary_variance = integrate_values( + points[boundary], + rowMeans((estimates[boundary, , drop = FALSE] - + mean_density[boundary])^2) + ) + ) +} + +for (scenario_index in seq_along(one_sided)) { + scenario <- one_sided[[scenario_index]] + points <- sort(unique(c( + 1e-10, + scenario$quantile(10^seq(-8, -1, length.out = 100L)), + scenario$quantile(seq(0.1, 0.9999, length.out = 401L)) + ))) + truth <- scenario$density(points) + boundary <- points <= scenario$quantile(0.1) + for (sample_size in sample_sizes) { + estimates <- matrix(NA_real_, length(points), replications) + for (replication in seq_len(replications)) { + set.seed(20260824L + 100000L * scenario_index + + 1000L * match(sample_size, sample_sizes) + replication) + fit <- kde1d(scenario$random(sample_size), xmin = 0) + estimates[, replication] <- dkde1d(points, fit) + result_rows[[length(result_rows) + 1L]] <- data.frame( + support = "one-sided", + scenario = names(one_sided)[[scenario_index]], + sample_size = sample_size, + replication = replication, + method = method, + global_ise = integrate_values( + points, (estimates[, replication] - truth)^2 + ), + boundary_ise = integrate_values( + points[boundary], + (estimates[boundary, replication] - truth[boundary])^2 + ), + edf = fit$edf, + loglik = fit$loglik + ) + } + summary_rows[[length(summary_rows) + 1L]] <- data.frame( + support = "one-sided", + scenario = names(one_sided)[[scenario_index]], + sample_size = sample_size, + method = method, + as.list(summarize_estimates(points, estimates, truth, boundary)) + ) + } +} + +points <- sort(unique(c( + 10^seq(-10, -2, length.out = 101L), + seq(0.01, 0.99, length.out = 301L), + 1 - 10^seq(-2, -10, length.out = 101L) +))) +boundary <- points <= 0.1 | points >= 0.9 +for (scenario_index in seq_along(two_sided)) { + shapes <- two_sided[[scenario_index]] + truth <- dbeta(points, shapes[[1L]], shapes[[2L]]) + for (sample_size in sample_sizes) { + estimates <- matrix(NA_real_, length(points), replications) + for (replication in seq_len(replications)) { + set.seed(20260825L + 100000L * scenario_index + + 1000L * match(sample_size, sample_sizes) + replication) + fit <- kde1d( + rbeta(sample_size, shapes[[1L]], shapes[[2L]]), + xmin = 0, + xmax = 1 + ) + estimates[, replication] <- dkde1d(points, fit) + result_rows[[length(result_rows) + 1L]] <- data.frame( + support = "two-sided", + scenario = names(two_sided)[[scenario_index]], + sample_size = sample_size, + replication = replication, + method = method, + global_ise = integrate_values( + points, (estimates[, replication] - truth)^2 + ), + boundary_ise = integrate_values( + points[boundary], + (estimates[boundary, replication] - truth[boundary])^2 + ), + edf = fit$edf, + loglik = fit$loglik + ) + } + summary_rows[[length(summary_rows) + 1L]] <- data.frame( + support = "two-sided", + scenario = names(two_sided)[[scenario_index]], + sample_size = sample_size, + method = method, + as.list(summarize_estimates(points, estimates, truth, boundary)) + ) + } +} + +dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) +write.csv(do.call(rbind, result_rows), output_file, row.names = FALSE) +write.csv( + do.call(rbind, summary_rows), + sub("\\.csv$", "-summary.csv", output_file), + row.names = FALSE +) From 0fcd5ccdf166adf488eaf7edc9555489d057dd07 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 15:19:37 +0200 Subject: [PATCH 08/25] Test boundary expert fallbacks --- test/test.cpp | 31 +++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) diff --git a/test/test.cpp b/test/test.cpp index 75acbb8..2a8e47d 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -253,6 +253,37 @@ TEST_CASE("two-sided exploding endpoints retain the bulk fit", CHECK(fit.get_edf() == Approx(bulk.get_edf()).epsilon(1e-12)); } +TEST_CASE("unsupported expert options retain the transformed bulk fit", + "[boundary-expert]") +{ + const Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + const Eigen::VectorXd observations = (-(1.0 - probabilities.array()).log()); + const Eigen::VectorXd weights = + Eigen::VectorXd::LinSpaced(observations.size(), 0.5, 1.5); + + Kde1d weighted(0.0, NAN, "continuous"); + weighted.fit(observations, weights); + Kde1d weighted_bulk(0.0, NAN, "continuous", 1.0, weighted.get_bandwidth()); + weighted_bulk.fit(observations, weights); + CHECK(weighted.get_values().isApprox(weighted_bulk.get_values(), 1e-12)); + CHECK(weighted.get_edf() == Approx(weighted_bulk.get_edf()).epsilon(1e-12)); + + Kde1d linear(0.0, NAN, "continuous", 1.0, NAN, 1); + linear.fit(observations); + Kde1d linear_bulk(0.0, NAN, "continuous", 1.0, linear.get_bandwidth(), 1); + linear_bulk.fit(observations); + CHECK(linear.get_values().isApprox(linear_bulk.get_values(), 1e-12)); + CHECK(linear.get_edf() == Approx(linear_bulk.get_edf()).epsilon(1e-12)); + + Kde1d small(0.0, NAN, "continuous"); + small.fit(observations.head(15)); + Kde1d small_bulk(0.0, NAN, "continuous", 1.0, small.get_bandwidth()); + small_bulk.fit(observations.head(15)); + CHECK(small.get_values().isApprox(small_bulk.get_values(), 1e-12)); + CHECK(small.get_edf() == Approx(small_bulk.get_edf()).epsilon(1e-12)); +} + TEST_CASE("finite support truncates density", "[finite-support]") { Eigen::VectorXd observations = Eigen::VectorXd::LinSpaced(200, 0.0, 1.0); From 61faced13c4b42e3b89962ed732673b6c85cc582 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 17:22:13 +0200 Subject: [PATCH 09/25] Simplify boundary expert implementation --- include/kde1d/kde1d.hpp | 351 +++++++++++++++++++++++----------------- 1 file changed, 199 insertions(+), 152 deletions(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 823c7b3..36fe127 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -124,7 +124,7 @@ class Kde1d struct BoundaryComponent { Eigen::VectorXd density; - Eigen::VectorXd response; + Eigen::VectorXd influence_num; }; // data members @@ -191,15 +191,14 @@ class Kde1d double multiplier, size_t degree, const Eigen::VectorXd& weights) const; - bool is_finite_endpoint(Eigen::VectorXd distances) const; - BoundaryComponent fit_boundary_component( - const Eigen::VectorXd& distances, - const Eigen::VectorXd& evaluation_distances, - const Eigen::VectorXd& bandwidth_weights, - double floor_fraction, - size_t degree) const; - void repair_boundaries(const Eigen::VectorXd& observations, - const Eigen::VectorXd& grid_points, + bool is_finite_endpoint(Eigen::VectorXd dist) const; + BoundaryComponent fit_boundary_component(const Eigen::VectorXd& dist, + const Eigen::VectorXd& eval_dist, + const Eigen::VectorXd& bw_weights, + double floor_fraction, + size_t degree) const; + void repair_boundaries(const Eigen::VectorXd& x, + const Eigen::VectorXd& grid, Eigen::VectorXd& influences); std::string as_str(VarType type) const; @@ -948,235 +947,283 @@ Kde1d::finalize_grid(Eigen::VectorXd& grid_points) return grid_points; } -//! Classifies a support endpoint from the power law of its closest order -//! statistics. Ambiguous and numerically degenerate cases retain the bulk fit. +//! Classifies a support endpoint from its ordered distances @f$d@f$ to the +//! endpoint. For @f$k = \min(n-1, \lceil 2\sqrt n \rceil)@f$, the lower-tail +//! index is +//! @f[ +//! \widehat\beta = \frac{k}{\sum_{i=1}^k +//! \log\{d_{(k+1)} / d_{(i)}\}}. +//! @f] +//! It is treated as finite when @f$\widehat\beta \geq 0.9@f$ and its +//! one-sided 95% lower confidence bound does not exceed one. Ambiguous and +//! numerically degenerate cases retain the bulk fit. +//! @param dist distances of the observations from the support endpoint; copied +//! because the classifier sorts them. +//! @return whether the endpoint is confidently classified as finite. inline bool -Kde1d::is_finite_endpoint(Eigen::VectorXd distances) const +Kde1d::is_finite_endpoint(Eigen::VectorXd dist) const { - std::sort(distances.data(), distances.data() + distances.size()); - const size_t tail_count = - std::min(static_cast(distances.size() - 1), - static_cast(std::ceil(2.0 * std::sqrt(distances.size())))); - const double threshold = distances(tail_count); - if (!(threshold > 0.0) || !std::isfinite(threshold)) + std::sort(dist.data(), dist.data() + dist.size()); + + // k is the number of lower order statistics; dist_k1 is d_(k+1). + const size_t k = + std::min(static_cast(dist.size() - 1), + static_cast(std::ceil(2.0 * std::sqrt(dist.size())))); + const double dist_k1 = dist(k); + if (!(dist_k1 > 0.0) || !std::isfinite(dist_k1)) return false; - double log_sum = 0.0; - const double distance_floor = - std::numeric_limits::epsilon() * threshold; - for (size_t index = 0; index < tail_count; ++index) { - log_sum += std::log(threshold / std::max(distances(index), distance_floor)); + // denom is the denominator of the lower-tail index beta = k / denom. + double denom = 0.0; + const double dist_min = std::numeric_limits::epsilon() * dist_k1; + for (size_t i = 0; i < k; ++i) { + denom += std::log(dist_k1 / std::max(dist(i), dist_min)); } - if (!(log_sum > 0.0) || !std::isfinite(log_sum)) + if (!(denom > 0.0) || !std::isfinite(denom)) return false; - const double tail_index = static_cast(tail_count) / log_sum; + const double beta = static_cast(k) / denom; // 1.64485 is the 95% standard-normal quantile used by the R selector. - return tail_index >= 0.9 && - tail_index * (1.0 - 1.6448536269514722 / std::sqrt(tail_count)) <= 1.0; + return beta >= 0.9 && beta * (1.0 - 1.6448536269514722 / std::sqrt(k)) <= 1.0; } -//! Fits one Gaussian local-polynomial endpoint component. Targeting weights -//! select its bandwidth only; equal observation contributions preserve the -//! original density estimand. +//! Fits a degree-@f$p@f$ Gaussian local-polynomial component from sample +//! distances @f$d@f$ to endpoint-distance grid @f$t@f$. With bandwidth +//! @f$h@f$, truncated Gaussian moments @f$\mu_r(a)@f$, and +//! @f$M_p(a) = [\mu_{j+k}(a)]_{j,k=0}^p@f$, the equivalent-kernel estimate is +//! @f[ +//! \begin{align*} +//! a &= t/h, & u_i &= (t-d_i)/h, \\[2pt] +//! \widehat f_p(t) +//! &= \frac{1}{nh}\sum_{i=1}^n \phi(u_i)\, +//! e_0^\mathsf{T} M_p(a)^{-1}(1,u_i,\ldots,u_i^p)^\mathsf{T}, \\[2pt] +//! \nu_p(t) &= \frac{\phi(0)}{nh} +//! e_0^\mathsf{T}M_p(a)^{-1}e_0. +//! \end{align*} +//! @f] +//! Targeting weights select @f$h@f$ only, so observations contribute equally +//! and the density estimand is unchanged. The influence numerator +//! @f$\nu_p(t)@f$ is the diagonal kernel contribution; dividing it by +//! @f$\widehat f_p(t)@f$ gives the pointwise influence used for EDF. +//! @param dist distances of the observations from the support endpoint. +//! @param eval_dist endpoint distances at which to evaluate the component. +//! @param bw_weights targeting weights used only for bandwidth selection. +//! @param floor_fraction fraction of the closest observations used to select +//! the bandwidth floor. +//! @param degree local-polynomial degree. +//! @return the normalized density and influence numerator on `eval_dist`; an +//! empty component indicates numerical failure. inline Kde1d::BoundaryComponent -Kde1d::fit_boundary_component(const Eigen::VectorXd& distances, - const Eigen::VectorXd& evaluation_distances, - const Eigen::VectorXd& bandwidth_weights, +Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, + const Eigen::VectorXd& eval_dist, + const Eigen::VectorXd& bw_weights, double floor_fraction, size_t degree) const { - bandwidth::PluginBandwidthSelector selector(distances, bandwidth_weights); - double bandwidth = selector.select_bandwidth(degree); - - Eigen::VectorXd ordered_distances = distances; - std::sort(ordered_distances.data(), - ordered_distances.data() + ordered_distances.size()); - const Eigen::Index floor_count = std::min( - distances.size(), + bandwidth::PluginBandwidthSelector selector(dist, bw_weights); + double h = selector.select_bandwidth(degree); + + // Floor h with a selector on the closest observations to stabilize the fit. + Eigen::VectorXd dist_sorted = dist; + std::sort(dist_sorted.data(), dist_sorted.data() + dist_sorted.size()); + const Eigen::Index n_floor = std::min( + dist.size(), std::max( - 4, - static_cast(std::ceil(floor_fraction * distances.size())))); - bandwidth::PluginBandwidthSelector floor_selector( - ordered_distances.head(floor_count)); - bandwidth = - std::max(bandwidth, floor_selector.select_bandwidth(degree)) * multiplier_; - if (!(bandwidth > 0.0) || !std::isfinite(bandwidth)) + 4, static_cast(std::ceil(floor_fraction * dist.size())))); + bandwidth::PluginBandwidthSelector floor_selector(dist_sorted.head(n_floor)); + h = std::max(h, floor_selector.select_bandwidth(degree)) * multiplier_; + if (!(h > 0.0) || !std::isfinite(h)) return {}; - BoundaryComponent component{ Eigen::VectorXd(evaluation_distances.size()), - Eigen::VectorXd(evaluation_distances.size()) }; - for (Eigen::Index row = 0; row < evaluation_distances.size(); ++row) { - const double boundary_position = evaluation_distances(row) / bandwidth; - const double normal_density = - K0_ * std::exp(-0.5 * boundary_position * boundary_position); - Eigen::VectorXd moments(2 * degree + 1); - moments(0) = - stats::pnorm(Eigen::VectorXd::Constant(1, boundary_position))(0); - moments(1) = -normal_density; - for (size_t order = 2; order < static_cast(moments.size()); - ++order) { - moments(order) = (order - 1.0) * moments(order - 2) - - std::pow(boundary_position, order - 1) * normal_density; + BoundaryComponent fit{ Eigen::VectorXd(eval_dist.size()), + Eigen::VectorXd(eval_dist.size()) }; + for (Eigen::Index j = 0; j < eval_dist.size(); ++j) { + // a = t/h truncates the kernel; mu stores its moments up to order 2p. + const double a = eval_dist(j) / h; + const double phi_a = K0_ * std::exp(-0.5 * a * a); + Eigen::VectorXd mu(2 * degree + 1); + mu(0) = stats::pnorm(Eigen::VectorXd::Constant(1, a))(0); + mu(1) = -phi_a; + for (size_t order = 2; order < static_cast(mu.size()); ++order) { + mu(order) = + (order - 1.0) * mu(order - 2) - std::pow(a, order - 1) * phi_a; } - Eigen::MatrixXd moment_matrix(degree + 1, degree + 1); + // M is the moment matrix; c, its first inverse row, gives the kernel. + Eigen::MatrixXd M(degree + 1, degree + 1); for (size_t column = 0; column <= degree; ++column) { - for (size_t matrix_row = 0; matrix_row <= degree; ++matrix_row) - moment_matrix(matrix_row, column) = moments(matrix_row + column); + for (size_t row = 0; row <= degree; ++row) + M(row, column) = mu(row + column); } - const Eigen::VectorXd coefficients = moment_matrix.inverse().row(0); - - double density = 0.0; - for (Eigen::Index observation = 0; observation < distances.size(); - ++observation) { - const double kernel_argument = - (evaluation_distances(row) - distances(observation)) / bandwidth; - double polynomial = coefficients(degree); + const Eigen::VectorXd c = M.inverse().row(0); + + double f = 0.0; + for (Eigen::Index i = 0; i < dist.size(); ++i) { + const double u = (eval_dist(j) - dist(i)) / h; + double p_u = c(degree); for (size_t order = degree; order > 0; --order) - polynomial = polynomial * kernel_argument + coefficients(order - 1); - density += - K0_ * std::exp(-0.5 * kernel_argument * kernel_argument) * polynomial; + p_u = p_u * u + c(order - 1); + f += K0_ * std::exp(-0.5 * u * u) * p_u; } - component.density(row) = - density / (static_cast(distances.size()) * bandwidth); - component.response(row) = - K0_ * coefficients(0) / - (static_cast(distances.size()) * bandwidth); + fit.density(j) = f / (static_cast(dist.size()) * h); + fit.influence_num(j) = K0_ * c(0) / (static_cast(dist.size()) * h); } - for (Eigen::Index row = 0; row < component.density.size(); ++row) { - if (!(component.density(row) > 0.0) || - !std::isfinite(component.density(row)) || - !std::isfinite(component.response(row))) { - component.density(row) = 0.0; - component.response(row) = 0.0; + // Remove unstable local-polynomial values, then normalize on the grid. + for (Eigen::Index j = 0; j < fit.density.size(); ++j) { + if (!(fit.density(j) > 0.0) || !std::isfinite(fit.density(j)) || + !std::isfinite(fit.influence_num(j))) { + fit.density(j) = 0.0; + fit.influence_num(j) = 0.0; } } double mass = 0.0; - for (Eigen::Index row = 0; row < component.density.size() - 1; ++row) { - mass += (evaluation_distances(row + 1) - evaluation_distances(row)) * - (component.density(row) + component.density(row + 1)) / 2.0; + for (Eigen::Index j = 0; j < fit.density.size() - 1; ++j) { + mass += (eval_dist(j + 1) - eval_dist(j)) * + (fit.density(j) + fit.density(j + 1)) / 2.0; } if (!(mass > 0.0) || !std::isfinite(mass)) return {}; - component.density /= mass; - component.response /= mass; - return component; + fit.density /= mass; + fit.influence_num /= mass; + return fit; } -//! Replaces the transformed bulk density near confidently finite endpoints -//! and carries the same local mixture through the diagonal EDF response. +//! Fuses the transformed bulk density @f$\widehat f_B@f$ with endpoint +//! densities @f$\widehat f_L@f$ and @f$\widehat f_U@f$. Each endpoint density +//! is the average of a local-linear and a local-quadratic estimate. Smooth +//! weights @f$w_L@f$ and @f$w_U@f$ are functions of the bulk CDF and shrink at +//! rate @f$\min(1/4,n^{-1/2})@f$: +//! @f[ +//! \begin{align*} +//! q &= \min(1/4,n^{-1/2}), & z(p) &= \min(1,p/q), \\[2pt] +//! g(p) &= 1-3z(p)^2+2z(p)^3, \\[2pt] +//! w_L &= g(F_B), & w_U &= g(1-F_B), \\[2pt] +//! \widehat f +//! &= w_L\widehat f_L+(1-w_L-w_U)\widehat f_B+w_U\widehat f_U, \\[2pt] +//! \nu &= w_L\nu_L+(1-w_L-w_U)\nu_B+w_U\nu_U, \\[2pt] +//! \mathrm{influence} &= \nu/\widehat f. +//! \end{align*} +//! @f] +//! Here @f$\nu@f$ is the influence numerator, i.e., the diagonal kernel +//! contribution on the density scale. Only endpoints classified as finite are +//! repaired. +//! @param x observations on the original scale. +//! @param grid increasing evaluation grid on the original scale. +//! @param influences on input, bulk-fit influences on `grid`; on output, +//! influences of the fused estimate. inline void -Kde1d::repair_boundaries(const Eigen::VectorXd& observations, - const Eigen::VectorXd& grid_points, +Kde1d::repair_boundaries(const Eigen::VectorXd& x, + const Eigen::VectorXd& grid, Eigen::VectorXd& influences) { - Eigen::VectorXd lower_distances; - Eigen::VectorXd upper_distances; + Eigen::VectorXd dist_lower; + Eigen::VectorXd dist_upper; bool repair_lower = !std::isnan(xmin_); bool repair_upper = !std::isnan(xmax_); if (repair_lower) { - lower_distances = observations.array() - xmin_; - repair_lower = is_finite_endpoint(lower_distances); + dist_lower = x.array() - xmin_; + repair_lower = is_finite_endpoint(dist_lower); } if (repair_upper) { - upper_distances = xmax_ - observations.array(); - repair_upper = is_finite_endpoint(upper_distances); + dist_upper = xmax_ - x.array(); + repair_upper = is_finite_endpoint(dist_upper); } if (!repair_lower && !repair_upper) return; - const double boundary_fraction = - std::min(0.25, 1.0 / std::sqrt(observations.size())); + // q is the shrinking probability width of each endpoint weight. + const double q = std::min(0.25, 1.0 / std::sqrt(x.size())); auto endpoint_weight = [&](double probability) { - const double position = std::min(1.0, probability / boundary_fraction); - return 1.0 - - (3.0 * position * position - 2.0 * position * position * position); + const double z = std::min(1.0, probability / q); + return 1.0 - (3.0 * z * z - 2.0 * z * z * z); }; - auto targeting_weights = [&](const Eigen::VectorXd& distances) { - Eigen::VectorXd weights(distances.size()); - const Eigen::VectorXi order = tools::get_order(distances); + // Mid-rank weights target endpoint observations during bandwidth selection. + auto targeting_weights = [&](const Eigen::VectorXd& dist) { + Eigen::VectorXd weights(dist.size()); + const Eigen::VectorXi order = tools::get_order(dist); Eigen::Index first = 0; while (first < order.size()) { Eigen::Index last = first; while (last + 1 < order.size() && - distances(order(last + 1)) == distances(order(first))) + dist(order(last + 1)) == dist(order(first))) ++last; const double probability = static_cast(first + last + 1) / - (2.0 * static_cast(distances.size())); - for (Eigen::Index index = first; index <= last; ++index) - weights(order(index)) = endpoint_weight(probability); + (2.0 * static_cast(dist.size())); + for (Eigen::Index i = first; i <= last; ++i) + weights(order(i)) = endpoint_weight(probability); first = last + 1; } return weights; }; + // The bandwidth floor uses all data on bounded support and 75% otherwise. const double floor_fraction = (!std::isnan(xmin_) && !std::isnan(xmax_)) ? 1.0 : 0.75; - auto fit_endpoint = [&](const Eigen::VectorXd& distances, - const Eigen::VectorXd& evaluation_distances) { - const Eigen::VectorXd weights = targeting_weights(distances); - BoundaryComponent linear = fit_boundary_component( - distances, evaluation_distances, weights, floor_fraction, 1); - BoundaryComponent quadratic = fit_boundary_component( - distances, evaluation_distances, weights, floor_fraction, 2); + auto fit_endpoint = [&](const Eigen::VectorXd& dist, + const Eigen::VectorXd& eval_dist) { + const Eigen::VectorXd bw_weights = targeting_weights(dist); + // Averaging orders one and two gives a smoother, more stable endpoint. + BoundaryComponent linear = + fit_boundary_component(dist, eval_dist, bw_weights, floor_fraction, 1); + BoundaryComponent quadratic = + fit_boundary_component(dist, eval_dist, bw_weights, floor_fraction, 2); if (linear.density.size() == 0 || quadratic.density.size() == 0) return BoundaryComponent{}; linear.density = (linear.density + quadratic.density) / 2.0; - linear.response = (linear.response + quadratic.response) / 2.0; + linear.influence_num = + (linear.influence_num + quadratic.influence_num) / 2.0; return linear; }; BoundaryComponent lower; BoundaryComponent upper; if (repair_lower) { - lower = fit_endpoint(lower_distances, grid_points.array() - xmin_); + lower = fit_endpoint(dist_lower, grid.array() - xmin_); repair_lower = lower.density.size() > 0; } if (repair_upper) { - Eigen::VectorXd evaluation_distances = - (xmax_ - grid_points.array()).reverse(); - upper = fit_endpoint(upper_distances, evaluation_distances); + Eigen::VectorXd upper_eval_dist = (xmax_ - grid.array()).reverse(); + upper = fit_endpoint(dist_upper, upper_eval_dist); repair_upper = upper.density.size() > 0; if (repair_upper) { upper.density.reverseInPlace(); - upper.response.reverseInPlace(); + upper.influence_num.reverseInPlace(); } } if (!repair_lower && !repair_upper) return; - const Eigen::VectorXd bulk_density = grid_.get_values(); - const Eigen::VectorXd probabilities = grid_.integrate(grid_points, true); - Eigen::VectorXd lower_weights = Eigen::VectorXd::Zero(grid_points.size()); - Eigen::VectorXd upper_weights = Eigen::VectorXd::Zero(grid_points.size()); - for (Eigen::Index row = 0; row < grid_points.size(); ++row) { - if (repair_lower) { - lower_weights(row) = endpoint_weight(probabilities(row)); - } - if (repair_upper) { - upper_weights(row) = endpoint_weight(1.0 - probabilities(row)); - } + // f_bulk and bulk_cdf determine the fused density and endpoint weights. + const Eigen::VectorXd f_bulk = grid_.get_values(); + const Eigen::VectorXd bulk_cdf = grid_.integrate(grid, true); + Eigen::VectorXd w_l = Eigen::VectorXd::Zero(grid.size()); + Eigen::VectorXd w_u = Eigen::VectorXd::Zero(grid.size()); + for (Eigen::Index j = 0; j < grid.size(); ++j) { + if (repair_lower) + w_l(j) = endpoint_weight(bulk_cdf(j)); + if (repair_upper) + w_u(j) = endpoint_weight(1.0 - bulk_cdf(j)); } - Eigen::VectorXd density(grid_points.size()); - Eigen::VectorXd response(grid_points.size()); - for (Eigen::Index row = 0; row < grid_points.size(); ++row) { - const double bulk_weight = 1.0 - lower_weights(row) - upper_weights(row); - density(row) = bulk_weight * bulk_density(row); - response(row) = bulk_weight * bulk_density(row) * influences(row); + // Fuse densities and influence numerators with the same weights. + Eigen::VectorXd f(grid.size()); + Eigen::VectorXd infl_num(grid.size()); + for (Eigen::Index j = 0; j < grid.size(); ++j) { + const double w_b = 1.0 - w_l(j) - w_u(j); + f(j) = w_b * f_bulk(j); + infl_num(j) = w_b * f_bulk(j) * influences(j); if (repair_lower) { - density(row) += lower_weights(row) * lower.density(row); - response(row) += lower_weights(row) * lower.response(row); + f(j) += w_l(j) * lower.density(j); + infl_num(j) += w_l(j) * lower.influence_num(j); } if (repair_upper) { - density(row) += upper_weights(row) * upper.density(row); - response(row) += upper_weights(row) * upper.response(row); + f(j) += w_u(j) * upper.density(j); + infl_num(j) += w_u(j) * upper.influence_num(j); } - influences(row) = density(row) > 0.0 ? response(row) / density(row) : 0.0; + influences(j) = f(j) > 0.0 ? infl_num(j) / f(j) : 0.0; } - grid_ = interp::InterpolationGrid(grid_points, density.cwiseMax(0.0), 3); + grid_ = interp::InterpolationGrid(grid, f.cwiseMax(0.0), 3); } // Bandwidth for Kernel Density Estimation From d957013ef4118242a0b5a00a071a5149a11d1da3 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 17:59:30 +0200 Subject: [PATCH 10/25] Speed up boundary expert evaluation --- diagnostic/NATIVE_RESULTS.md | 56 ++++-- diagnostic/boundary-repair/HANDOFF.md | 9 +- diagnostic/boundary-repair/README.md | 15 +- diagnostic/one-sided-repair/HANDOFF.md | 4 +- diagnostic/one-sided-repair/NATIVE_CPP.md | 107 +++++------ diagnostic/one-sided-repair/README.md | 17 +- include/kde1d/kde1d.hpp | 218 +++++++++------------- test/test.cpp | 10 +- 8 files changed, 210 insertions(+), 226 deletions(-) diff --git a/diagnostic/NATIVE_RESULTS.md b/diagnostic/NATIVE_RESULTS.md index 8067ea6..18cd011 100644 --- a/diagnostic/NATIVE_RESULTS.md +++ b/diagnostic/NATIVE_RESULTS.md @@ -34,10 +34,41 @@ Beta$(2,0.75)$ has 1.027/1.026. Gamma$(2)$ and Beta$(2,2)$ select bulk in every large-sample replication and are exactly unchanged. Uniform, Beta$(1,2)$, and Beta$(2,1)$ have $n=2000$ global ratios 0.844, 0.817, and 0.830. -The deterministic native tests agree with the retained R reference values to -within $2\times10^{-4}$ relative tolerance and cover lower/upper reflection, -independent two-sided endpoint decisions, exploding/vanishing fallback, and -affine support changes. +The deterministic native tests cover lower/upper reflection, independent +two-sided endpoint decisions, exploding/vanishing fallback, and affine support +changes. Their golden values were refreshed for the simplified evaluator. + +## Runtime simplification ablation + +The direct native evaluator was simplified after the main validation. The +local-linear and local-quadratic equivalent kernels now share the degree-2 +bandwidth and are averaged in one observation loop. On bounded support this +bandwidth uses all endpoint distances; on one-sided support it uses the closest +75%. Endpoint kernels are evaluated only where their smooth fusion weights are +nonzero, Gaussian terms beyond six bandwidths are omitted, and the fused grid +is normalized once at the end. + +A paired 100-replication check compared this implementation with commit +`cbde530` over Exponential, half-normal, Gamma$(2)$, Gamma$(0.75)$, Lomax$(2)$, +Uniform, Beta$(1,2)$, Beta$(0.75,2)$, Beta$(0.75,0.75)$, and Beta$(2,2)$. +Ratios compare the simplified evaluator with `cbde530`; parentheses contain +paired Monte Carlo standard errors: + +| support | $n$ | global ISE ratio | boundary ISE ratio | +|---|---:|---:|---:| +| one-sided | 25 | 0.996 (0.002) | 0.999 (0.004) | +| one-sided | 100 | 0.983 (0.003) | 0.982 (0.003) | +| one-sided | 1000 | 0.993 (0.003) | 0.992 (0.003) | +| one-sided | 2000 | 0.992 (0.003) | 0.991 (0.003) | +| two-sided | 25 | 1.010 (0.003) | 1.014 (0.006) | +| two-sided | 100 | 0.999 (0.002) | 1.002 (0.004) | +| two-sided | 1000 | 0.999 (0.003) | 0.992 (0.004) | +| two-sided | 2000 | 0.994 (0.003) | 0.986 (0.004) | + +The largest scenario-level increases were about 3.5% for Gamma$(0.75)$ and +3.9% for Beta$(0.75,0.75)$; Uniform, Beta$(1,2)$, Exponential, half-normal, +and Lomax generally improved. This supports the simpler shared-bandwidth +kernel average without a material aggregate accuracy cost. ## EDF check @@ -51,24 +82,23 @@ For deterministic finite-endpoint samples at $n=25,50,100$, the discrepancy was 0.08--0.30 EDF units for Uniform and Exponential examples. The asymmetric Beta$(1,2)$ discrepancy was 0.27--0.33 at $n=50,100$ and 0.84 at $n=25$. This is adequate for the existing asymptotic EDF convention and does not -justify a gate-derivative correction. Pure-bulk fits retain the old EDF +justify a weight-derivative correction. Pure-bulk fits retain the old EDF exactly. ## Fit time Release builds were timed against `4f3d148`. Bulk-classified fits incur only -sorting and remained within about 3% of baseline for $n=100$--$2000$. Active -experts cost more because the concise implementation directly evaluates the -Gaussian kernels on the 401-point grid: +sorting and remain close to baseline. With a 401-point output grid, the +simplified active-expert timings are: | active endpoints | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:| -| one | 1.70 ms (4.4x) | 5.93 ms (12.4x) | 10.67 ms (18.5x) | -| two | 2.90 ms (7.5x) | 10.41 ms (23.5x) | 18.84 ms (36.7x) | +| one | 0.65 ms (1.7x) | 0.94 ms (2.0x) | 1.22 ms (2.1x) | +| two | 0.78 ms (2.0x) | 1.63 ms (3.7x) | 2.26 ms (4.4x) | -The absolute cost remains below 20 ms at $n=2000$. Keep the direct evaluator -for the first PR; optimize only if downstream profiling shows fit time is -material. +Relative to `cbde530`, this is a speedup of 2.6--8.7x for one active endpoint +and 3.7--8.3x for two. Absolute expert-fit cost remains below 2.3 ms at +$n=2000$ in this benchmark. ## Reproduction diff --git a/diagnostic/boundary-repair/HANDOFF.md b/diagnostic/boundary-repair/HANDOFF.md index 92a57ed..3d66ef0 100644 --- a/diagnostic/boundary-repair/HANDOFF.md +++ b/diagnostic/boundary-repair/HANDOFF.md @@ -4,9 +4,10 @@ The directory now contains one experimental estimator for continuous data with two known finite bounds. It fits the current probit bulk estimator once, -adds an equal local-linear/local-quadratic expert for confidently finite -endpoints, and otherwise reuses bulk. Smooth CDF-scale gates shrink as -$n^{-1/2}$. The finite-endpoint classifier uses +adds an averaged local-linear/local-quadratic kernel expert for confidently +finite endpoints, and otherwise reuses bulk. The kernels share one degree-2 +bandwidth and smooth CDF-scale weights shrink as $n^{-1/2}$. The +finite-endpoint classifier uses $k=\min(n-1,\lceil2\sqrt n\rceil)$ order statistics and a 95% decision. There is no exploding-tail expert, power warp, transformation offset, or CV @@ -33,7 +34,7 @@ as the first two arguments to either simulation script. - The R reference assumes support $[0,1]$; native code must apply an affine map for arbitrary finite bounds. - Weighted observations have not been specified or validated for the tail - index, weighted ranks, or shrinking gate. + index or shrinking weights. - The finite-versus-bulk decision is hard, so between-sample endpoint behavior can still change discretely. - Before release, test affine support changes, weaker and stronger endpoint diff --git a/diagnostic/boundary-repair/README.md b/diagnostic/boundary-repair/README.md index ee49a6c..0fbb4e6 100644 --- a/diagnostic/boundary-repair/README.md +++ b/diagnostic/boundary-repair/README.md @@ -8,7 +8,7 @@ current probit estimator, and the retained endpoint-classifier ablation. The reference implementation assumes the support has been mapped affinely to $[0,1]$. First fit the current unweighted probit estimator $\widehat f_B$ and -use its CDF to define sample-shrinking endpoint gates. With +use its CDF to define sample-shrinking endpoint weights. With $r_n=\min(0.25,n^{-1/2})$ and $s(t)=3t^2-2t^3$, $$ @@ -17,11 +17,12 @@ w_L(x)=1-s\left(\min\left\{1,\frac{\widehat F_B(x)}{r_n}\right\}\right), w_U(x)=1-s\left(\min\left\{1,\frac{1-\widehat F_B(x)}{r_n}\right\}\right), $$ -and $w_B(x)=1-w_L(x)-w_U(x)$. The finite-boundary expert is the -equal average of Gaussian equivalent-kernel local-linear and local-quadratic -estimates. Rank-based endpoint weights select their bandwidths, but density -contributions remain unweighted, so the estimand does not change. Negative -component values are truncated during normalization. +and $w_B(x)=1-w_L(x)-w_U(x)$. The finite-boundary expert averages Gaussian +equivalent-kernel local-linear and local-quadratic kernels using one degree-2 +bandwidth selected from all endpoint distances. Density contributions remain +unweighted, so the estimand does not change. The native evaluator computes the +expert only where its fusion weight is nonzero, truncates negative values, and +normalizes once after fusion. Finite endpoint behavior is identified from $k=\min(n-1,\lceil2\sqrt n\rceil)$ order statistics. At the lower endpoint, @@ -46,7 +47,7 @@ offset transform, oversmoothed tail expert, or cross-validation selector. ## Retained files -- `scripts/bounded_estimator.R`: self-contained R reference implementation. +- `scripts/bounded_estimator.R`: pre-native tuning implementation. - `scripts/validate_bounded_estimator.R`: paired validation against current. - `scripts/plot_bounded_estimator_validation.R`: numerical and realization report. diff --git a/diagnostic/one-sided-repair/HANDOFF.md b/diagnostic/one-sided-repair/HANDOFF.md index edf56af..be19ba3 100644 --- a/diagnostic/one-sided-repair/HANDOFF.md +++ b/diagnostic/one-sided-repair/HANDOFF.md @@ -3,10 +3,10 @@ The production branch already uses a scale-equivariant power-$3/4$ transform for one-sided supports. The diagnostic candidate keeps that estimator as the unweighted bulk and adds the selected two-boundary method's finite expert: -equal local-linear/local-quadratic estimates, a shrinking CDF gate, and a +an averaged local-linear/local-quadratic kernel, a shrinking CDF weight, and a $2\sqrt n$ order-statistic finite-versus-bulk decision. -The bandwidth floor is the unweighted bandwidth fitted to the lowest 75% of +The native kernels share the degree-2 bandwidth fitted to the lowest 75% of boundary distances. A 30-replication ablation compared fixed fractions from 15% through 100% and a $\sqrt n$ shrinking subset. Performance improved up to 75%; using all observations reversed the long-tail gains because remote Lomax diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md index 1983ec9..745f051 100644 --- a/diagnostic/one-sided-repair/NATIVE_CPP.md +++ b/diagnostic/one-sided-repair/NATIVE_CPP.md @@ -41,7 +41,7 @@ the bulk grid: 2. return to the unchanged bulk path if no endpoint is confidently finite; 3. fit a boundary component only for each selected endpoint, using the existing original-scale grid; -4. form gate probabilities from the normalized bulk CDF; +4. form endpoint weights from the normalized bulk CDF; 5. fuse bulk and selected endpoint values and replace `grid_` with the normalized fused grid. @@ -50,7 +50,7 @@ log-likelihood code then operates on the fused grid. `bandwidth_` continues to report the bulk bandwidth. Boundary distances and local densities can stay in the original units. Every -classifier ratio is dimensionless, and both selected and floor bandwidths +classifier ratio is dimensionless, and the boundary bandwidths scale with the data, so this is equivalent to the R reference's affine map to $[0,1]$ without adding a second normalization path. @@ -95,14 +95,12 @@ The helper takes boundary distances, ascending evaluation distances, rank weights, a floor fraction, and degree one or two. - Select the weighted bandwidth with `PluginBandwidthSelector`. -- Select the unweighted floor bandwidth from the closest +- Select one unweighted degree-2 bandwidth from the closest $\max(4,\lceil q n\rceil)$ distances, where $q=0.75$ for one-sided support and $q=1$ for two-sided support. -- Use the maximum of the selected and floor bandwidths, then apply the public - multiplier. -- Use rank weights only for bandwidth selection. Evaluate density - contributions with equal observation weights so the estimand remains the - original density. +- Share it between the degree-one and degree-two kernels, then apply the public + multiplier. Evaluate density contributions with equal observation weights + so the estimand remains the original density. Construct the equivalent-kernel coefficients as the first row of the inverse truncated-normal moment matrix. Generate the moments with @@ -113,24 +111,20 @@ $$ \mu_j(a)=(j-1)\mu_{j-2}(a)-a^{j-1}\phi(a). $$ -This calculation covers degrees one and two more concisely than separate -determinant formulas. Clamp each component at zero, normalize it on the -distance grid, and average the degree-one and degree-two components. Return -both that density and its diagonal density response for the EDF calculation -described below; the response uses the same clamp mask and normalization as -the density. +Use the explicit degree-one and degree-two determinants to avoid a dynamic +matrix inverse at every evaluation point. Average the two kernels before +fusion, clamp negative values, and return both the density and its influence +numerator for the EDF calculation described below. -Start with direct $O(nm)$ Gaussian evaluation on the existing grid of -$m\approx401$ points. It follows the retained R references closely and avoids -a second interpolation grid or FFT-specific derivation. Benchmark before -considering an optimized implementation. +Evaluate directly only where the endpoint weight is nonzero. With ordered +distances, omit observations more than six bandwidths from an evaluation +point; the omitted Gaussian tail mass is below $2\times10^{-9}$. Normalize the +fused grid once at the end. ### 3. Boundary-repair coordinator -This helper owns endpoint distances, average ranks for ties, classification, -local component calls, CDF gates, reflection, and fusion. Use -`tools::get_order()` locally; do not add a general ranking API unless another -production caller needs it. +This helper owns endpoint distances, classification, local component calls, +CDF weights, reflection, and fusion. For an upper endpoint, compute on ascending reflected distances and reverse the component once. The floor fraction is the only local-component policy that @@ -139,7 +133,7 @@ differs between one- and two-sided support. The helper should return an empty result when every endpoint selects bulk. `Kde1d::fit()` can then leave the already constructed bulk grid untouched. -## Gate and fusion +## Weights and fusion Let $F_B(x)$ be the bulk CDF and @@ -161,7 +155,7 @@ $$ w_U(x)=1-s\left(\min\{1,(1-F_B(x))/q_n\}\right). $$ -Set the gate of every bulk-classified endpoint to zero. The final values are +Set the weight of every bulk-classified endpoint to zero. The final values are $$ \widehat f(x)= @@ -170,7 +164,7 @@ w_L(x)\widehat f_L(x) +w_U(x)\widehat f_U(x). $$ -With $q_n\leq0.25$, the endpoint gates do not overlap. The same expression +With $q_n\leq0.25$, the endpoint weights do not overlap. The same expression covers one-sided support by setting the absent endpoint weight to zero. Clamp the fused values at zero and construct a normalized `InterpolationGrid` on the existing original-scale grid. @@ -182,15 +176,14 @@ holds the selected bandwidth and final grid normalization fixed. Extend the same convention to expert selection and fusion rather than returning `NaN`. For a degree-$p$ boundary component, let $M_p(a)$ be the truncated-normal -moment matrix above, let $h_p$ be its final bandwidth, let $Z_p$ be the mass -used to normalize its nonnegative density, and let $\widetilde f_p$ denote its -value before clamping and normalization. Its diagonal density response is +moment matrix above, let $h$ be the shared bandwidth, and let +$\widetilde f_p$ denote its value before clamping. Its influence numerator is $$ -r_p(x)= -\frac{\mathbf 1\{\widetilde f_p(x)>0\}}{Z_p} -\frac{\phi(0)}{n h_p} -\left[M_p\{d(x)/h_p\}^{-1}\right]_{00}. +\nu_p(x)= +\mathbf 1\{\widetilde f_p(x)>0\} +\frac{\phi(0)}{n h} +\left[M_p\{d(x)/h\}^{-1}\right]_{00}. $$ Only the constant equivalent-kernel coefficient remains because a @@ -200,26 +193,26 @@ expert, use $$ f_E(x)=\frac{f_1(x)+f_2(x)}{2}, \qquad -r_E(x)=\frac{r_1(x)+r_2(x)}{2}. +\nu_E(x)=\frac{\nu_1(x)+\nu_2(x)}{2}. $$ For the bulk component, the existing influence column is its log-density -leverage $\ell_B(x)$, so its diagonal density response is -$r_B(x)=f_B(x)\ell_B(x)$. Fuse the responses with exactly the same gates as the -densities: +leverage $\ell_B(x)$, so its influence numerator is +$\nu_B(x)=f_B(x)\ell_B(x)$. Fuse the numerators with exactly the same weights +as the densities: $$ \begin{aligned} g(x)&=w_L(x)f_L(x) +\{1-w_L(x)-w_U(x)\}f_B(x)+w_U(x)f_U(x),\\ -r(x)&=w_L(x)r_L(x) - +\{1-w_L(x)-w_U(x)\}r_B(x)+w_U(x)r_U(x),\\ -\ell(x)&=\frac{r(x)}{g(x)}. +\nu(x)&=w_L(x)\nu_L(x) + +\{1-w_L(x)-w_U(x)\}\nu_B(x)+w_U(x)\nu_U(x),\\ +\ell(x)&=\frac{\nu(x)}{g(x)}. \end{aligned} $$ Thus the mixture leverage is weighted by local density shares, not just by -the gate values. Estimate +the fusion weights. Estimate $$ \operatorname{edf}=\sum_{i=1}^n @@ -227,10 +220,10 @@ $$ $$ retaining the current per-observation cap. The final common normalization of -$g$ and $r$ cancels in their ratio when its derivative is ignored. +$g$ and $\nu$ cancels in their ratio when its derivative is ignored. This approximation conditions on bandwidths, endpoint classifications, CDF -gates, clamp states, and normalization constants. It deliberately omits the +weights, clamp states, and normalization constants. It deliberately omits the derivatives of those data-adaptive choices. That keeps it consistent with the existing EDF convention and costs only additional grid-vector arithmetic; no refits or per-observation matrices are needed. Validate it diagnostically @@ -242,24 +235,23 @@ $$ $$ First confirm that this diagnostic reproduces the existing bulk EDF to the -expected approximation error. A gate-derivative correction is worth +expected approximation error. A weight-derivative correction is worth considering only if the active-expert comparison then shows an additional systematic discrepancy. ## Weights and remaining fit metadata -The experts' rank weights affect bandwidth selection only; density -contributions remain equally weighted, matching the validated estimand. The -first native implementation falls back to bulk when public case weights are -supplied because those weights genuinely change the estimand. Defining -weighted ranks, effective sample size, weighted tail indices, and weighted -confidence adjustments is a separate statistical task. +Expert density contributions remain equally weighted, matching the validated +estimand. The native implementation falls back to bulk when public case +weights are supplied because those weights genuinely change the estimand. +Defining effective sample size, weighted tail indices, and weighted confidence +adjustments is a separate statistical task. Recompute `loglik_` from the final grid using the existing code. Use the conditional mixture trace above for `edf_` whenever a finite expert is active, and retain the current calculation unchanged for pure-bulk fits. -No classifier choice, tail index, boundary bandwidth, or gate state needs to +No classifier choice, tail index, boundary bandwidth, or weight state needs to persist in the fitted object for the first implementation. Diagnostic values belong in tests and validation scripts rather than the public class layout. @@ -271,7 +263,7 @@ The intended implementation footprint is: - preserve original-scale cleaned observations; - add the three private helpers; - call the coordinator after bulk-grid construction; - - carry the bulk and expert diagonal responses through fusion for EDF. + - carry the bulk and expert influence numerators through fusion for EDF. 2. `test/test.cpp` - deterministic golden results and fallback behavior. 3. `test/test_numerical_invariants.cpp` @@ -317,18 +309,17 @@ the initial implementation remains reviewable. ### Public case weights -Public case weights change the target density, unlike the endpoint-targeting -weights used only to select expert bandwidths. A weighted expert should -therefore use public case weights for density contributions and use the product -of public and endpoint-targeting weights for bandwidth selection. Before -activation, compare and validate choices for: +Public case weights change the target density. A weighted expert should +therefore use public case weights for density contributions and define the +bandwidth subset by cumulative public weight. Before activation, compare and +validate choices for: -- weighted average ranks and endpoint distances; +- weighted endpoint distances; - effective sample size in $k$, $q_n$, and the classifier confidence term; - a weighted order-statistic tail index; - defining the closest 75% floor by cumulative public weight rather than row count; -- weighted diagonal responses and EDF validation. +- weighted influence numerators and EDF validation. Experiments should include highly unequal weights, weights concentrated near and far from the boundary, zero weights, global rescaling of all weights, and diff --git a/diagnostic/one-sided-repair/README.md b/diagnostic/one-sided-repair/README.md index 1fa174d..41b2b56 100644 --- a/diagnostic/one-sided-repair/README.md +++ b/diagnostic/one-sided-repair/README.md @@ -9,15 +9,16 @@ with exactly one known finite endpoint. It is deliberately separate from The power-$3/4$ transformation estimator is the unweighted bulk fit. A single order-statistic tail index classifies the finite endpoint using $k=\min(n-1,\lceil2\sqrt n\rceil)$ and the same 95% rule as in the -two-boundary estimator. A confidently finite endpoint receives the equal -local-linear/local-quadratic expert; exploding, vanishing, and ambiguous +two-boundary estimator. A confidently finite endpoint receives the averaged +local-linear/local-quadratic kernel expert; exploding, vanishing, and ambiguous endpoints reuse bulk. -The boundary expert is blended with bulk through a smooth gate based on the -bulk CDF, with boundary probability $\min(0.25,n^{-1/2})$. Its local-polynomial -bandwidth is floored at the unweighted bandwidth fitted to the lowest 75% of -boundary distances. This preserves the stabilizing information in most of the -sample without allowing the most remote observations to dominate the floor. +The boundary expert is blended with bulk through a smooth weight based on the +bulk CDF, with boundary probability $\min(0.25,n^{-1/2})$. Both kernels share +the degree-2 bandwidth fitted to the closest 75% of boundary distances. The +native evaluator only computes expert values where this weight is nonzero and +normalizes once after fusion. This preserves the stabilizing information in +most of the sample without allowing the most remote observations to dominate. The construction is reflection- and scale-equivariant. The validation suite uses 30 paired replications at $n=100,1000$ for @@ -27,7 +28,7 @@ have been removed. ## Files -- `scripts/one_sided_estimator.R`: current R reference implementation. +- `scripts/one_sided_estimator.R`: pre-native tuning implementation. - `scripts/ablate_local_floor_fraction.R`: selected floor-fraction ablation. - `scripts/plot_local_floor_fraction_ablation.R`: tuning curves and example estimates. diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 36fe127..f979a77 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -194,9 +194,7 @@ class Kde1d bool is_finite_endpoint(Eigen::VectorXd dist) const; BoundaryComponent fit_boundary_component(const Eigen::VectorXd& dist, const Eigen::VectorXd& eval_dist, - const Eigen::VectorXd& bw_weights, - double floor_fraction, - size_t degree) const; + double bandwidth) const; void repair_boundaries(const Eigen::VectorXd& x, const Eigen::VectorXd& grid, Eigen::VectorXd& influences); @@ -987,89 +985,75 @@ Kde1d::is_finite_endpoint(Eigen::VectorXd dist) const return beta >= 0.9 && beta * (1.0 - 1.6448536269514722 / std::sqrt(k)) <= 1.0; } -//! Fits a degree-@f$p@f$ Gaussian local-polynomial component from sample -//! distances @f$d@f$ to endpoint-distance grid @f$t@f$. With bandwidth -//! @f$h@f$, truncated Gaussian moments @f$\mu_r(a)@f$, and -//! @f$M_p(a) = [\mu_{j+k}(a)]_{j,k=0}^p@f$, the equivalent-kernel estimate is +//! Fits the average of Gaussian local-linear and local-quadratic equivalent +//! kernels from sample distances @f$d@f$ to endpoint-distance grid @f$t@f$. +//! For degree @f$p@f$, shared bandwidth @f$h@f$, truncated Gaussian moments +//! @f$\mu_r(a)@f$, and @f$M_p(a)=[\mu_{j+k}(a)]_{j,k=0}^p@f$, //! @f[ //! \begin{align*} //! a &= t/h, & u_i &= (t-d_i)/h, \\[2pt] -//! \widehat f_p(t) +//! \widehat f_p(t;h) //! &= \frac{1}{nh}\sum_{i=1}^n \phi(u_i)\, -//! e_0^\mathsf{T} M_p(a)^{-1}(1,u_i,\ldots,u_i^p)^\mathsf{T}, \\[2pt] -//! \nu_p(t) &= \frac{\phi(0)}{nh} -//! e_0^\mathsf{T}M_p(a)^{-1}e_0. +//! e_0^\mathsf{T}M_p(a)^{-1} +//! (1,u_i,\ldots,u_i^p)^\mathsf{T}, \\[2pt] +//! \widehat f_\partial(t) +//! &= \{\widehat f_1(t;h)+\widehat f_2(t;h)\}/2. //! \end{align*} //! @f] -//! Targeting weights select @f$h@f$ only, so observations contribute equally -//! and the density estimand is unchanged. The influence numerator -//! @f$\nu_p(t)@f$ is the diagonal kernel contribution; dividing it by -//! @f$\widehat f_p(t)@f$ gives the pointwise influence used for EDF. -//! @param dist distances of the observations from the support endpoint. +//! Observations contribute equally to both kernels. The returned influence +//! numerator is the corresponding average diagonal kernel contribution. +//! @param dist ordered distances of the observations from the support endpoint. //! @param eval_dist endpoint distances at which to evaluate the component. -//! @param bw_weights targeting weights used only for bandwidth selection. -//! @param floor_fraction fraction of the closest observations used to select -//! the bandwidth floor. -//! @param degree local-polynomial degree. -//! @return the normalized density and influence numerator on `eval_dist`; an -//! empty component indicates numerical failure. +//! @param bandwidth shared bandwidth of both equivalent kernels. +//! @return the density and influence numerator on `eval_dist`. inline Kde1d::BoundaryComponent Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, const Eigen::VectorXd& eval_dist, - const Eigen::VectorXd& bw_weights, - double floor_fraction, - size_t degree) const + double bandwidth) const { - bandwidth::PluginBandwidthSelector selector(dist, bw_weights); - double h = selector.select_bandwidth(degree); - - // Floor h with a selector on the closest observations to stabilize the fit. - Eigen::VectorXd dist_sorted = dist; - std::sort(dist_sorted.data(), dist_sorted.data() + dist_sorted.size()); - const Eigen::Index n_floor = std::min( - dist.size(), - std::max( - 4, static_cast(std::ceil(floor_fraction * dist.size())))); - bandwidth::PluginBandwidthSelector floor_selector(dist_sorted.head(n_floor)); - h = std::max(h, floor_selector.select_bandwidth(degree)) * multiplier_; + const double h = bandwidth; if (!(h > 0.0) || !std::isfinite(h)) return {}; BoundaryComponent fit{ Eigen::VectorXd(eval_dist.size()), Eigen::VectorXd(eval_dist.size()) }; for (Eigen::Index j = 0; j < eval_dist.size(); ++j) { - // a = t/h truncates the kernel; mu stores its moments up to order 2p. + // c1 and c2 are the first inverse-moment rows for degrees 1 and 2. const double a = eval_dist(j) / h; - const double phi_a = K0_ * std::exp(-0.5 * a * a); - Eigen::VectorXd mu(2 * degree + 1); - mu(0) = stats::pnorm(Eigen::VectorXd::Constant(1, a))(0); - mu(1) = -phi_a; - for (size_t order = 2; order < static_cast(mu.size()); ++order) { - mu(order) = - (order - 1.0) * mu(order - 2) - std::pow(a, order - 1) * phi_a; - } - - // M is the moment matrix; c, its first inverse row, gives the kernel. - Eigen::MatrixXd M(degree + 1, degree + 1); - for (size_t column = 0; column <= degree; ++column) { - for (size_t row = 0; row <= degree; ++row) - M(row, column) = mu(row + column); - } - const Eigen::VectorXd c = M.inverse().row(0); + const double phi = K0_ * std::exp(-0.5 * a * a); + const double mu0 = 0.5 * std::erfc(-a * 0.7071067811865475); + const double mu1 = -phi; + const double mu2 = mu0 - a * phi; + const double mu3 = -(a * a + 2.0) * phi; + const double mu4 = 3.0 * mu0 - (a * a * a + 3.0 * a) * phi; + const double det1 = mu0 * mu2 - mu1 * mu1; + const double c10 = mu2 / det1; + const double c11 = -mu1 / det1; + const double det2 = mu0 * (mu2 * mu4 - mu3 * mu3) - + mu1 * (mu1 * mu4 - mu2 * mu3) + + mu2 * (mu1 * mu3 - mu2 * mu2); + const double c20 = (mu2 * mu4 - mu3 * mu3) / det2; + const double c21 = (mu2 * mu3 - mu1 * mu4) / det2; + const double c22 = (mu1 * mu3 - mu2 * mu2) / det2; double f = 0.0; - for (Eigen::Index i = 0; i < dist.size(); ++i) { - const double u = (eval_dist(j) - dist(i)) / h; - double p_u = c(degree); - for (size_t order = degree; order > 0; --order) - p_u = p_u * u + c(order - 1); - f += K0_ * std::exp(-0.5 * u * u) * p_u; + // Six Gaussian standard deviations leave less than 2e-9 tail mass. + const double radius = 6.0 * h; + const double* first = std::lower_bound( + dist.data(), dist.data() + dist.size(), eval_dist(j) - radius); + const double* last = std::upper_bound( + dist.data(), dist.data() + dist.size(), eval_dist(j) + radius); + for (const double* value = first; value != last; ++value) { + const double u = (eval_dist(j) - *value) / h; + f += K0_ * std::exp(-0.5 * u * u) * + (c10 + c11 * u + c20 + (c21 + c22 * u) * u) / h; } - fit.density(j) = f / (static_cast(dist.size()) * h); - fit.influence_num(j) = K0_ * c(0) / (static_cast(dist.size()) * h); + fit.density(j) = f / (2.0 * static_cast(dist.size())); + fit.influence_num(j) = + K0_ * (c10 + c20) / (2.0 * static_cast(dist.size()) * h); } - // Remove unstable local-polynomial values, then normalize on the grid. + // Remove unstable local-polynomial values. for (Eigen::Index j = 0; j < fit.density.size(); ++j) { if (!(fit.density(j) > 0.0) || !std::isfinite(fit.density(j)) || !std::isfinite(fit.influence_num(j))) { @@ -1077,23 +1061,15 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, fit.influence_num(j) = 0.0; } } - double mass = 0.0; - for (Eigen::Index j = 0; j < fit.density.size() - 1; ++j) { - mass += (eval_dist(j + 1) - eval_dist(j)) * - (fit.density(j) + fit.density(j + 1)) / 2.0; - } - if (!(mass > 0.0) || !std::isfinite(mass)) - return {}; - fit.density /= mass; - fit.influence_num /= mass; return fit; } //! Fuses the transformed bulk density @f$\widehat f_B@f$ with endpoint //! densities @f$\widehat f_L@f$ and @f$\widehat f_U@f$. Each endpoint density -//! is the average of a local-linear and a local-quadratic estimate. Smooth -//! weights @f$w_L@f$ and @f$w_U@f$ are functions of the bulk CDF and shrink at -//! rate @f$\min(1/4,n^{-1/2})@f$: +//! averages local-linear and local-quadratic kernels using one degree-2 +//! bandwidth, selected from all distances on bounded support and the closest +//! 75% on one-sided support. Smooth weights @f$w_L@f$ and @f$w_U@f$ are +//! functions of the bulk CDF and shrink at rate @f$\min(1/4,n^{-1/2})@f$: //! @f[ //! \begin{align*} //! q &= \min(1/4,n^{-1/2}), & z(p) &= \min(1,p/q), \\[2pt] @@ -1138,74 +1114,57 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, const double z = std::min(1.0, probability / q); return 1.0 - (3.0 * z * z - 2.0 * z * z * z); }; - // Mid-rank weights target endpoint observations during bandwidth selection. - auto targeting_weights = [&](const Eigen::VectorXd& dist) { - Eigen::VectorXd weights(dist.size()); - const Eigen::VectorXi order = tools::get_order(dist); - Eigen::Index first = 0; - while (first < order.size()) { - Eigen::Index last = first; - while (last + 1 < order.size() && - dist(order(last + 1)) == dist(order(first))) - ++last; - const double probability = static_cast(first + last + 1) / - (2.0 * static_cast(dist.size())); - for (Eigen::Index i = first; i <= last; ++i) - weights(order(i)) = endpoint_weight(probability); - first = last + 1; - } - return weights; - }; - // The bandwidth floor uses all data on bounded support and 75% otherwise. - const double floor_fraction = + // Only evaluate endpoint fits where their fusion weights are nonzero. + const Eigen::VectorXd f_bulk = grid_.get_values(); + const Eigen::VectorXd bulk_cdf = grid_.integrate(grid, true); + Eigen::VectorXd w_l = Eigen::VectorXd::Zero(grid.size()); + Eigen::VectorXd w_u = Eigen::VectorXd::Zero(grid.size()); + for (Eigen::Index j = 0; j < grid.size(); ++j) { + if (repair_lower) + w_l(j) = endpoint_weight(bulk_cdf(j)); + if (repair_upper) + w_u(j) = endpoint_weight(1.0 - bulk_cdf(j)); + } + const Eigen::Index n_lower = (w_l.array() > 0.0).count(); + const Eigen::Index n_upper = (w_u.array() > 0.0).count(); + + // Select one shared degree-2 bandwidth, using the local 75% one-sided rule. + const double bw_fraction = (!std::isnan(xmin_) && !std::isnan(xmax_)) ? 1.0 : 0.75; + Eigen::VectorXd bw_dist = repair_lower ? dist_lower : dist_upper; + std::sort(bw_dist.data(), bw_dist.data() + bw_dist.size()); + const Eigen::Index n_bw = std::min( + bw_dist.size(), + std::max( + 4, static_cast(std::ceil(bw_fraction * bw_dist.size())))); + bandwidth::PluginBandwidthSelector selector(bw_dist.head(n_bw)); + const double h = selector.select_bandwidth(2) * multiplier_; + auto fit_endpoint = [&](const Eigen::VectorXd& dist, const Eigen::VectorXd& eval_dist) { - const Eigen::VectorXd bw_weights = targeting_weights(dist); - // Averaging orders one and two gives a smoother, more stable endpoint. - BoundaryComponent linear = - fit_boundary_component(dist, eval_dist, bw_weights, floor_fraction, 1); - BoundaryComponent quadratic = - fit_boundary_component(dist, eval_dist, bw_weights, floor_fraction, 2); - if (linear.density.size() == 0 || quadratic.density.size() == 0) - return BoundaryComponent{}; - linear.density = (linear.density + quadratic.density) / 2.0; - linear.influence_num = - (linear.influence_num + quadratic.influence_num) / 2.0; - return linear; + Eigen::VectorXd dist_sorted = dist; + std::sort(dist_sorted.data(), dist_sorted.data() + dist_sorted.size()); + return fit_boundary_component(dist_sorted, eval_dist, h); }; BoundaryComponent lower; BoundaryComponent upper; + repair_lower = repair_lower && n_lower > 0; + repair_upper = repair_upper && n_upper > 0; if (repair_lower) { - lower = fit_endpoint(dist_lower, grid.array() - xmin_); + lower = fit_endpoint(dist_lower, grid.head(n_lower).array() - xmin_); repair_lower = lower.density.size() > 0; } if (repair_upper) { - Eigen::VectorXd upper_eval_dist = (xmax_ - grid.array()).reverse(); + Eigen::VectorXd upper_eval_dist = + (xmax_ - grid.tail(n_upper).array()).reverse(); upper = fit_endpoint(dist_upper, upper_eval_dist); repair_upper = upper.density.size() > 0; - if (repair_upper) { - upper.density.reverseInPlace(); - upper.influence_num.reverseInPlace(); - } } if (!repair_lower && !repair_upper) return; - // f_bulk and bulk_cdf determine the fused density and endpoint weights. - const Eigen::VectorXd f_bulk = grid_.get_values(); - const Eigen::VectorXd bulk_cdf = grid_.integrate(grid, true); - Eigen::VectorXd w_l = Eigen::VectorXd::Zero(grid.size()); - Eigen::VectorXd w_u = Eigen::VectorXd::Zero(grid.size()); - for (Eigen::Index j = 0; j < grid.size(); ++j) { - if (repair_lower) - w_l(j) = endpoint_weight(bulk_cdf(j)); - if (repair_upper) - w_u(j) = endpoint_weight(1.0 - bulk_cdf(j)); - } - // Fuse densities and influence numerators with the same weights. Eigen::VectorXd f(grid.size()); Eigen::VectorXd infl_num(grid.size()); @@ -1213,13 +1172,14 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, const double w_b = 1.0 - w_l(j) - w_u(j); f(j) = w_b * f_bulk(j); infl_num(j) = w_b * f_bulk(j) * influences(j); - if (repair_lower) { + if (w_l(j) > 0.0) { f(j) += w_l(j) * lower.density(j); infl_num(j) += w_l(j) * lower.influence_num(j); } - if (repair_upper) { - f(j) += w_u(j) * upper.density(j); - infl_num(j) += w_u(j) * upper.influence_num(j); + if (w_u(j) > 0.0) { + const Eigen::Index upper_j = grid.size() - 1 - j; + f(j) += w_u(j) * upper.density(upper_j); + infl_num(j) += w_u(j) * upper.influence_num(upper_j); } influences(j) = f(j) > 0.0 ? infl_num(j) / f(j) : 0.0; } diff --git a/test/test.cpp b/test/test.cpp index 2a8e47d..a61d7f5 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -148,8 +148,8 @@ TEST_CASE("one-sided finite endpoints use the boundary expert", CHECK((fit.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > 0.01); Eigen::VectorXd expected_density(6); - expected_density << 0.9905722, 0.9905911, 0.9885084, 0.9473293, 0.7314338, - 0.0077356; + expected_density << 0.9884817, 0.9885018, 0.9865198, 0.9465577, 0.7315411, + 0.0077367; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(4), fit.get_values()(24), fit.get_values()(49), fit.get_values()(99), @@ -194,8 +194,8 @@ TEST_CASE("two-sided finite endpoints use the boundary experts", CHECK((fit.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > 0.01); Eigen::VectorXd expected_density(6); - expected_density << 1.0368661, 1.0367788, 1.0250191, 0.9972352, 1.0231640, - 1.0368661; + expected_density << 0.9993158, 0.9992803, 0.9985546, 1.0001208, 0.9985473, + 0.9993158; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(49), fit.get_values()(99), fit.get_values()(199), fit.get_values()(299), @@ -223,7 +223,7 @@ TEST_CASE("two-sided endpoints are classified independently", fit.fit(observations); Eigen::VectorXd expected_density(6); - expected_density << 1.9952890, 1.9913280, 1.9839701, 0.9946680, 0.0562144, + expected_density << 1.9984196, 1.9944352, 1.9846050, 0.9946111, 0.0562112, 0.0000020; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(49), From 75409b92c97b0d3a4916fba55c7bea512ef5a277 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 18:18:07 +0200 Subject: [PATCH 11/25] Speed up boundary kernels with FFT --- diagnostic/NATIVE_RESULTS.md | 26 ++++++++++++++++ include/kde1d/kde1d.hpp | 58 ++++++++++++++++++++++++++---------- test/test.cpp | 8 +++-- 3 files changed, 75 insertions(+), 17 deletions(-) diff --git a/diagnostic/NATIVE_RESULTS.md b/diagnostic/NATIVE_RESULTS.md index 18cd011..f39455f 100644 --- a/diagnostic/NATIVE_RESULTS.md +++ b/diagnostic/NATIVE_RESULTS.md @@ -100,6 +100,32 @@ Relative to `cbde530`, this is a speedup of 2.6--8.7x for one active endpoint and 3.7--8.3x for two. Absolute expert-fit cost remains below 2.3 ms at $n=2000$ in this benchmark. +### FFT evaluation + +The endpoint kernel can be written as a pointwise combination of an ordinary +Gaussian KDE and its first two derivatives. The implementation now evaluates +these three translation-invariant convolutions on a regular 256-bin grid and +interpolates them to the endpoint grid. + +Against the direct endpoint evaluator, total fit times with the default +401-point grid were: + +| active endpoints | $n$ | direct | FFT | speedup | +|---|---:|---:|---:|---:| +| one | 1000 | 0.93 ms | 0.78 ms | 1.19x | +| one | 2000 | 1.21 ms | 0.92 ms | 1.32x | +| two | 1000 | 1.62 ms | 0.84 ms | 1.93x | +| two | 2000 | 2.25 ms | 0.96 ms | 2.35x | + +The direct-kernel fallback was removed after a separate $n=25,100$ benchmark. +Across 51--401 grid points, the worst total-fit slowdown from always using FFT +was 1.25x. With the default grid at $n=100$, one endpoint slowed from 0.64 to +0.67 ms while two endpoints improved slightly from 0.77 to 0.74 ms. In the +100-replication validation suite, the mean relative ISE perturbation from FFT +binning was at most 0.011% for every support/sample-size group. Among fits +whose endpoint expert was active, the median absolute paired ISE change was +0.023%, the 99th percentile was 0.18%, and the maximum was 0.66%. + ## Reproduction Install the package with a clean native rebuild at each revision and run diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index f979a77..2f3e7e5 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -1000,6 +1000,17 @@ Kde1d::is_finite_endpoint(Eigen::VectorXd dist) const //! &= \{\widehat f_1(t;h)+\widehat f_2(t;h)\}/2. //! \end{align*} //! @f] +//! Writing @f$f^{(r)}@f$ for the @f$r@f$th derivative of the ordinary +//! Gaussian KDE and @f$c_{pj}@f$ for the entries of the first row of +//! @f$M_p(a)^{-1}@f$, the same estimator is +//! @f[ +//! \begin{align*} +//! \widehat f_\partial(t) +//! &= \frac{1}{2}\{(c_{10}+c_{20}+c_{22})f(t) +//! -h(c_{11}+c_{21})f^{(1)}(t)+h^2c_{22}f^{(2)}(t)\}. +//! \end{align*} +//! @f] +//! This identity evaluates the three convolutions by FFT. //! Observations contribute equally to both kernels. The returned influence //! numerator is the corresponding average diagonal kernel contribution. //! @param dist ordered distances of the observations from the support endpoint. @@ -1015,8 +1026,29 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, if (!(h > 0.0) || !std::isfinite(h)) return {}; - BoundaryComponent fit{ Eigen::VectorXd(eval_dist.size()), - Eigen::VectorXd(eval_dist.size()) }; + BoundaryComponent fit{ Eigen::VectorXd::Zero(eval_dist.size()), + Eigen::VectorXd::Zero(eval_dist.size()) }; + if (eval_dist.size() == 0) + return fit; + + // Compute the ordinary Gaussian KDE and its first two derivatives on a + // regular grid, then interpolate them to the endpoint grid. + const double fft_upper = eval_dist(eval_dist.size() - 1) + 6.0 * h; + const double* last = + std::upper_bound(dist.data(), dist.data() + dist.size(), fft_upper); + const Eigen::Index n_fft = last - dist.data(); + if (n_fft == 0) + return fit; + + // This resolution kept the worst paired ISE perturbation below 0.7%. + const size_t num_bins = 256; + fft::KdeFFT kde_fft( + dist.head(n_fft), h, 0.0, fft_upper, Eigen::VectorXd(), num_bins); + const double scale = + static_cast(n_fft) / static_cast(dist.size()); + const Eigen::VectorXd f0 = scale * kde_fft.kde_drv(0); + const Eigen::VectorXd f1 = scale * kde_fft.kde_drv(1); + const Eigen::VectorXd f2 = scale * kde_fft.kde_drv(2); for (Eigen::Index j = 0; j < eval_dist.size(); ++j) { // c1 and c2 are the first inverse-moment rows for degrees 1 and 2. const double a = eval_dist(j) / h; @@ -1036,19 +1068,15 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, const double c21 = (mu2 * mu3 - mu1 * mu4) / det2; const double c22 = (mu1 * mu3 - mu2 * mu2) / det2; - double f = 0.0; - // Six Gaussian standard deviations leave less than 2e-9 tail mass. - const double radius = 6.0 * h; - const double* first = std::lower_bound( - dist.data(), dist.data() + dist.size(), eval_dist(j) - radius); - const double* last = std::upper_bound( - dist.data(), dist.data() + dist.size(), eval_dist(j) + radius); - for (const double* value = first; value != last; ++value) { - const double u = (eval_dist(j) - *value) / h; - f += K0_ * std::exp(-0.5 * u * u) * - (c10 + c11 * u + c20 + (c21 + c22 * u) * u) / h; - } - fit.density(j) = f / (2.0 * static_cast(dist.size())); + const double position = eval_dist(j) * num_bins / fft_upper; + const size_t bin = std::min(static_cast(position), num_bins - 1); + const double fraction = position - static_cast(bin); + auto interpolate = [&](const Eigen::VectorXd& values) { + return (1.0 - fraction) * values(bin) + fraction * values(bin + 1); + }; + fit.density(j) = + 0.5 * ((c10 + c20 + c22) * interpolate(f0) - + h * (c11 + c21) * interpolate(f1) + h * h * c22 * interpolate(f2)); fit.influence_num(j) = K0_ * (c10 + c20) / (2.0 * static_cast(dist.size()) * h); } diff --git a/test/test.cpp b/test/test.cpp index a61d7f5..75c684e 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -119,10 +119,14 @@ TEST_CASE("boundary grids resolve the transformed support", "[boundary-grid]") TEST_CASE("one-boundary fits are reflection equivariant", "[boundary-reflection]") { Eigen::VectorXd observations = Eigen::VectorXd::LinSpaced(500, 0.01, 5.0); - Kde1d left_bounded(0.0, NAN, "continuous", 1.0, 0.5); + Kde1d left_bounded(0.0, NAN, "continuous"); left_bounded.fit(observations); + Kde1d bulk(0.0, NAN, "continuous", 1.0, left_bounded.get_bandwidth()); + bulk.fit(observations); + CHECK((left_bounded.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > + 0.01); - Kde1d right_bounded(NAN, 0.0, "continuous", 1.0, 0.5); + Kde1d right_bounded(NAN, 0.0, "continuous"); right_bounded.fit(-observations); CHECK(left_bounded.get_grid_points().isApprox( From 8c49a1f247d1b11043258b254049525c720ee2ad Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 19:31:51 +0200 Subject: [PATCH 12/25] Support manual bandwidth boundary repair --- include/kde1d/kde1d.hpp | 7 +++---- test/test.cpp | 20 +++++++++----------- 2 files changed, 12 insertions(+), 15 deletions(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 2f3e7e5..e3794cb 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -342,13 +342,12 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) Eigen::VectorXd w = weights; tools::remove_nans(xx, w); - // Nonconstant case weights and manual bandwidths need separate expert - // semantics; constant weights are equivalent to an unweighted sample. + // Nonconstant case weights need separate expert semantics; constant weights + // are equivalent to an unweighted sample. const bool unweighted = w.size() == 0 || w.minCoeff() == w.maxCoeff(); const bool use_boundary_repair = type_ == VarType::continuous && xx.size() >= 16 && unweighted && - std::isnan(bandwidth_spec_) && degree_ == 2 && - (!std::isnan(xmin_) || !std::isnan(xmax_)); + degree_ == 2 && (!std::isnan(xmin_) || !std::isnan(xmax_)); Eigen::VectorXd boundary_observations; if (use_boundary_repair) boundary_observations = xx; diff --git a/test/test.cpp b/test/test.cpp index 75c684e..fa574ff 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -121,10 +121,9 @@ TEST_CASE("one-boundary fits are reflection equivariant", "[boundary-reflection] Eigen::VectorXd observations = Eigen::VectorXd::LinSpaced(500, 0.01, 5.0); Kde1d left_bounded(0.0, NAN, "continuous"); left_bounded.fit(observations); - Kde1d bulk(0.0, NAN, "continuous", 1.0, left_bounded.get_bandwidth()); - bulk.fit(observations); - CHECK((left_bounded.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > - 0.01); + Kde1d manual(0.0, NAN, "continuous", 1.0, left_bounded.get_bandwidth()); + manual.fit(observations); + CHECK(left_bounded.get_values().isApprox(manual.get_values(), 1e-12)); Kde1d right_bounded(NAN, 0.0, "continuous"); right_bounded.fit(-observations); @@ -146,10 +145,9 @@ TEST_CASE("one-sided finite endpoints use the boundary expert", Kde1d fit(0.0, NAN, "continuous"); fit.fit(observations); - // A manual fit with the selected bulk bandwidth bypasses boundary repair. - Kde1d bulk(0.0, NAN, "continuous", 1.0, fit.get_bandwidth()); - bulk.fit(observations); - CHECK((fit.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > 0.01); + Kde1d manual(0.0, NAN, "continuous", 1.0, fit.get_bandwidth()); + manual.fit(observations); + CHECK(fit.get_values().isApprox(manual.get_values(), 1e-12)); Eigen::VectorXd expected_density(6); expected_density << 0.9884817, 0.9885018, 0.9865198, 0.9465577, 0.7315411, @@ -193,9 +191,9 @@ TEST_CASE("two-sided finite endpoints use the boundary experts", Kde1d fit(0.0, 1.0, "continuous"); fit.fit(observations); - Kde1d bulk(0.0, 1.0, "continuous", 1.0, fit.get_bandwidth()); - bulk.fit(observations); - CHECK((fit.get_values() - bulk.get_values()).cwiseAbs().maxCoeff() > 0.01); + Kde1d manual(0.0, 1.0, "continuous", 1.0, fit.get_bandwidth()); + manual.fit(observations); + CHECK(fit.get_values().isApprox(manual.get_values(), 1e-12)); Eigen::VectorXd expected_density(6); expected_density << 0.9993158, 0.9992803, 0.9985546, 1.0001208, 0.9985473, From 7c51bfcd05b3292e645b020146f19497d2e8a3f7 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 19:34:36 +0200 Subject: [PATCH 13/25] Support weighted boundary repair --- diagnostic/one-sided-repair/NATIVE_CPP.md | 126 +++++++--------- include/kde1d/kde1d.hpp | 174 +++++++++++++++------- test/test.cpp | 43 +++++- 3 files changed, 209 insertions(+), 134 deletions(-) diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md index 745f051..76a351c 100644 --- a/diagnostic/one-sided-repair/NATIVE_CPP.md +++ b/diagnostic/one-sided-repair/NATIVE_CPP.md @@ -13,24 +13,20 @@ path: The existing transformed estimator remains the bulk component in both cases. Unbounded continuous, discrete, and zero-inflated behavior remains unchanged. -The first native version should activate only for samples of at least 16 -observations, unweighted or constant-weight fits, an automatically selected -bandwidth, and the default degree two. Nonconstant weighted fits, explicit -bandwidths, and nondefault degrees retain the current estimator until -their expert semantics have been specified and validated. This is the first -implementation milestone, not the intended final support boundary: experiments -and subsequent activation for weighted and manual-bandwidth fits are important -follow-up work. Keep the bandwidth multiplier supported immediately by -applying it to every expert bandwidth after selection and flooring. +The production estimator activates for degree-two continuous fits with at least +16 observations and effective sample size at least 16. Public case weights and +manual bandwidths are supported. Nondefault degrees retain the transformed +bulk estimator pending separate evaluation. Apply the bandwidth multiplier to +every expert bandwidth after selection and flooring. Do not add a public method switch or another fitted-object representation. ## Minimal integration point Call the repair coordinator only when `type_ == VarType::continuous`, at least -one support bound is finite, at least 16 cleaned observations remain, case -weights are absent or constant, `bandwidth_spec_` is `NaN`, and `degree_ == 2`. -This makes every initial fallback condition explicit at a single call site. +one support bound is finite, at least 16 cleaned observations remain, and +`degree_ == 2`. The coordinator additionally retains the bulk fit when the +effective sample size is below 16. Keep the current body of `Kde1d::fit()` through construction of the normalized bulk `InterpolationGrid`. Preserve the cleaned observations on their original @@ -241,11 +237,13 @@ systematic discrepancy. ## Weights and remaining fit metadata -Expert density contributions remain equally weighted, matching the validated -estimand. The native implementation falls back to bulk when public case -weights are supplied because those weights genuinely change the estimand. -Defining effective sample size, weighted tail indices, and weighted confidence -adjustments is a separate statistical task. +Expert density contributions use the normalized public case weights, matching +the weighted bulk estimand. Effective sample size determines the minimum sample +check, fusion width, tail order, and classifier confidence. The weighted +classifier uses a conservative lower threshold of 0.975. The one-sided +bandwidth uses the closest 75% of positive-weight observations by row count and +passes their case weights to the plug-in selector. The influence numerator uses +the local average case weight on the FFT grid. Recompute `loglik_` from the final grid using the existing code. Use the conditional mixture trace above for `edf_` whenever a finite expert is active, @@ -300,63 +298,43 @@ public getters unless implementation evidence shows that it is necessary. Each step should be a separately testable commit. Avoid refactoring unrelated fit logic while implementing the method. -## Important follow-up: weights and manual bandwidths - -Do not close the estimator work after the initial unweighted, automatic- -bandwidth activation. Keep the following experiments and production activation -as explicit roadmap items, preferably in follow-up commits or a follow-up PR so -the initial implementation remains reviewable. - -### Public case weights - -Public case weights change the target density. A weighted expert should -therefore use public case weights for density contributions and define the -bandwidth subset by cumulative public weight. Before activation, compare and -validate choices for: - -- weighted endpoint distances; -- effective sample size in $k$, $q_n$, and the classifier confidence term; -- a weighted order-statistic tail index; -- defining the closest 75% floor by cumulative public weight rather than row - count; -- weighted influence numerators and EDF validation. - -Experiments should include highly unequal weights, weights concentrated near -and far from the boundary, zero weights, global rescaling of all weights, and -integer weights compared with explicitly replicated observations. Require -weight-scale invariance, approximate replication equivalence, stable endpoint -classification, and acceptable global/boundary ISE before removing the -weighted fallback. - -### Manually specified bandwidths - -A manual bulk bandwidth is expressed on the transformed scale, whereas local -boundary bandwidths are expressed in original data units. Reusing the same -number for both is therefore invalid. The leading candidate is to compute the -automatic bulk reference bandwidth $h_{B,0}$ and interpret the manual choice -$h_B$ through the dimensionless ratio - -$$ -\rho=\frac{h_B}{h_{B,0}}, -$$ - -then multiply every automatically selected and floored expert bandwidth by -$\rho$. This preserves the requested bulk bandwidth while treating it as a -global smoothing adjustment. Compare this with leaving expert bandwidths -automatic when only the bulk bandwidth is manual; reject direct numerical -reuse across scales. - -Run the comparison over manual-to-automatic ratios such as $0.5$, $0.75$, $1$, -$1.5$, and $2$, several support rescalings, both support types, finite and -exploding endpoint shapes, and representative visual fits. Include the extra -cost of computing $h_{B,0}$ in the manual case. Activate manual-bandwidth fits -only after selecting and documenting one interpretation that preserves affine -equivariance and behaves predictably with `multiplier_`. - -Finally test weighted and manual bandwidths together after each has been -validated separately. Nondefault local-likelihood degrees remain a lower- -priority extension because the selected boundary expert deliberately averages -degrees one and two. +## Weighted and manual-bandwidth resolution + +Manual bandwidths control only the transformed bulk fit. Boundary bandwidths +remain independently selected in original data units, exactly as when the bulk +bandwidth is automatic. The public multiplier remains the common smoothing +control and scales both bulk and expert bandwidths. + +Weighted experiments rejected defining the one-sided 75% bandwidth subset by +cumulative weight: concentrated weights made that subset too narrow and +unstable. Counting positive-weight observations was both simpler and more +accurate. Effective sample size gave a small but consistent improvement for the +fusion width under concentrated weights. A weighted classifier threshold of +0.975 avoided most false repair of exploding targets while retaining the +finite-boundary gains. Global weight rescaling and insertion or removal of +zero-weight observations are numerically invariant. + +Integer-weight replication equivalence is not required here because the +existing bulk bandwidth selector interprets public weights through effective +sample size rather than as frequency counts. Supporting frequency weights +would require a separate change to the bulk estimator's weight semantics. + +### Required follow-up: degrees zero and one + +Keep boundary-expert activation for `degree_ < 2` as an important open task. +The current estimator must continue to retain the transformed bulk fit for +these degrees until this is evaluated. Compare at least: + +- retaining the averaged local-linear/local-quadratic boundary expert for all + bulk degrees; +- matching the endpoint expert to the requested bulk degree; +- using local linear at the endpoint for both degree-zero and degree-one bulk + fits. + +Evaluate global and boundary ISE, bias and variance, visual boundary stability, +EDF behavior, and runtime for both support types, including weighted and manual- +bandwidth fits. Do not activate degrees zero or one based only on API symmetry; +the selected degree-two expert deliberately averages degrees one and two. ## Native tests diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index e3794cb..b29afd3 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -191,13 +191,17 @@ class Kde1d double multiplier, size_t degree, const Eigen::VectorXd& weights) const; - bool is_finite_endpoint(Eigen::VectorXd dist) const; - BoundaryComponent fit_boundary_component(const Eigen::VectorXd& dist, - const Eigen::VectorXd& eval_dist, - double bandwidth) const; + bool is_finite_endpoint(const Eigen::VectorXd& dist, + const Eigen::VectorXd& weights) const; + BoundaryComponent fit_boundary_component( + const Eigen::VectorXd& dist, + const Eigen::VectorXd& eval_dist, + double bandwidth, + const Eigen::VectorXd& weights) const; void repair_boundaries(const Eigen::VectorXd& x, const Eigen::VectorXd& grid, - Eigen::VectorXd& influences); + Eigen::VectorXd& influences, + const Eigen::VectorXd& weights); std::string as_str(VarType type) const; VarType as_enum(std::string type) const; @@ -342,12 +346,9 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) Eigen::VectorXd w = weights; tools::remove_nans(xx, w); - // Nonconstant case weights need separate expert semantics; constant weights - // are equivalent to an unweighted sample. - const bool unweighted = w.size() == 0 || w.minCoeff() == w.maxCoeff(); - const bool use_boundary_repair = - type_ == VarType::continuous && xx.size() >= 16 && unweighted && - degree_ == 2 && (!std::isnan(xmin_) || !std::isnan(xmax_)); + const bool use_boundary_repair = type_ == VarType::continuous && + xx.size() >= 16 && degree_ == 2 && + (!std::isnan(xmin_) || !std::isnan(xmax_)); Eigen::VectorXd boundary_observations; if (use_boundary_repair) boundary_observations = xx; @@ -423,7 +424,7 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) // (3 iterations for normalization to a proper density) grid_ = interp::InterpolationGrid(grid_points, values, 3); if (use_boundary_repair) - repair_boundaries(boundary_observations, grid_points, influences); + repair_boundaries(boundary_observations, grid_points, influences, w); // calculate log-likelihood of final estimate xx = boundary_transform(xx, true); @@ -951,37 +952,53 @@ Kde1d::finalize_grid(Eigen::VectorXd& grid_points) //! \widehat\beta = \frac{k}{\sum_{i=1}^k //! \log\{d_{(k+1)} / d_{(i)}\}}. //! @f] -//! It is treated as finite when @f$\widehat\beta \geq 0.9@f$ and its -//! one-sided 95% lower confidence bound does not exceed one. Ambiguous and +//! It is treated as finite when @f$\widehat\beta \geq 0.9@f$ and its one-sided +//! 95% lower confidence bound does not exceed one. The weighted threshold is +//! 0.975 to avoid unstable repair of exploding targets. Ambiguous and //! numerically degenerate cases retain the bulk fit. -//! @param dist distances of the observations from the support endpoint; copied -//! because the classifier sorts them. +//! With nonconstant case weights, their effective sample size replaces @f$n@f$ +//! and the lower tail is defined by cumulative normalized weight. +//! @param dist ordered distances of the observations from the support endpoint. +//! @param weights correspondingly ordered case weights with mean one. //! @return whether the endpoint is confidently classified as finite. inline bool -Kde1d::is_finite_endpoint(Eigen::VectorXd dist) const +Kde1d::is_finite_endpoint(const Eigen::VectorXd& dist, + const Eigen::VectorXd& weights) const { - std::sort(dist.data(), dist.data() + dist.size()); + const double n_eff = weights.sum() * weights.sum() / weights.squaredNorm(); + if (!(n_eff > 1.0) || !std::isfinite(n_eff)) + return false; - // k is the number of lower order statistics; dist_k1 is d_(k+1). - const size_t k = - std::min(static_cast(dist.size() - 1), - static_cast(std::ceil(2.0 * std::sqrt(dist.size())))); - const double dist_k1 = dist(k); + // Scale weights to effective counts and locate the (k+1)th weighted order + // statistic, where k = min(n_eff, ceil(2 sqrt(n_eff))). + const Eigen::VectorXd counts = weights * n_eff / weights.sum(); + const double target = + std::min(std::nextafter(n_eff, 0.0), std::ceil(2.0 * std::sqrt(n_eff))); + Eigen::Index k1 = 0; + double cumulative = counts(0); + while (cumulative <= target && k1 + 1 < dist.size()) + cumulative += counts(++k1); + const double dist_k1 = dist(k1); if (!(dist_k1 > 0.0) || !std::isfinite(dist_k1)) return false; - // denom is the denominator of the lower-tail index beta = k / denom. + // tail_mass and denom define the weighted lower-tail index beta. + double tail_mass = 0.0; double denom = 0.0; const double dist_min = std::numeric_limits::epsilon() * dist_k1; - for (size_t i = 0; i < k; ++i) { - denom += std::log(dist_k1 / std::max(dist(i), dist_min)); + for (Eigen::Index i = 0; i < k1; ++i) { + tail_mass += counts(i); + denom += counts(i) * std::log(dist_k1 / std::max(dist(i), dist_min)); } - if (!(denom > 0.0) || !std::isfinite(denom)) + if (!(tail_mass > 0.0) || !(denom > 0.0) || !std::isfinite(denom)) return false; - const double beta = static_cast(k) / denom; + const double beta = tail_mass / denom; // 1.64485 is the 95% standard-normal quantile used by the R selector. - return beta >= 0.9 && beta * (1.0 - 1.6448536269514722 / std::sqrt(k)) <= 1.0; + const double beta_min = + weights.minCoeff() == weights.maxCoeff() ? 0.9 : 0.975; + return beta >= beta_min && + beta * (1.0 - 1.6448536269514722 / std::sqrt(tail_mass)) <= 1.0; } //! Fits the average of Gaussian local-linear and local-quadratic equivalent @@ -992,7 +1009,7 @@ Kde1d::is_finite_endpoint(Eigen::VectorXd dist) const //! \begin{align*} //! a &= t/h, & u_i &= (t-d_i)/h, \\[2pt] //! \widehat f_p(t;h) -//! &= \frac{1}{nh}\sum_{i=1}^n \phi(u_i)\, +//! &= \frac{1}{nh}\sum_{i=1}^n w_i\phi(u_i)\, //! e_0^\mathsf{T}M_p(a)^{-1} //! (1,u_i,\ldots,u_i^p)^\mathsf{T}, \\[2pt] //! \widehat f_\partial(t) @@ -1010,16 +1027,18 @@ Kde1d::is_finite_endpoint(Eigen::VectorXd dist) const //! \end{align*} //! @f] //! This identity evaluates the three convolutions by FFT. -//! Observations contribute equally to both kernels. The returned influence -//! numerator is the corresponding average diagonal kernel contribution. +//! Both kernels use the same normalized case weights @f$w_i@f$. The returned +//! influence numerator is the corresponding average diagonal contribution. //! @param dist ordered distances of the observations from the support endpoint. //! @param eval_dist endpoint distances at which to evaluate the component. //! @param bandwidth shared bandwidth of both equivalent kernels. +//! @param weights correspondingly ordered case weights with mean one. //! @return the density and influence numerator on `eval_dist`. inline Kde1d::BoundaryComponent Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, const Eigen::VectorXd& eval_dist, - double bandwidth) const + double bandwidth, + const Eigen::VectorXd& weights) const { const double h = bandwidth; if (!(h > 0.0) || !std::isfinite(h)) @@ -1036,18 +1055,27 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, const double* last = std::upper_bound(dist.data(), dist.data() + dist.size(), fft_upper); const Eigen::Index n_fft = last - dist.data(); - if (n_fft == 0) + const double fft_weight = weights.head(n_fft).sum(); + if (n_fft == 0 || !(fft_weight > 0.0)) return fit; // This resolution kept the worst paired ISE perturbation below 0.7%. const size_t num_bins = 256; fft::KdeFFT kde_fft( - dist.head(n_fft), h, 0.0, fft_upper, Eigen::VectorXd(), num_bins); - const double scale = - static_cast(n_fft) / static_cast(dist.size()); + dist.head(n_fft), h, 0.0, fft_upper, weights.head(n_fft), num_bins); + const double scale = fft_weight / weights.sum(); const Eigen::VectorXd f0 = scale * kde_fft.kde_drv(0); const Eigen::VectorXd f1 = scale * kde_fft.kde_drv(1); const Eigen::VectorXd f2 = scale * kde_fft.kde_drv(2); + Eigen::VectorXd local_weight = Eigen::VectorXd::Ones(num_bins + 1); + if (weights.minCoeff() != weights.maxCoeff()) { + const Eigen::VectorXd count = tools::linbin( + dist.head(n_fft), 0.0, fft_upper, num_bins, Eigen::VectorXd::Ones(n_fft)); + local_weight = (count.array() == 0.0) + .select(Eigen::VectorXd::Zero(count.size()), + weights.head(n_fft).mean() * + kde_fft.get_bin_counts().cwiseQuotient(count)); + } for (Eigen::Index j = 0; j < eval_dist.size(); ++j) { // c1 and c2 are the first inverse-moment rows for degrees 1 and 2. const double a = eval_dist(j) / h; @@ -1076,8 +1104,8 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, fit.density(j) = 0.5 * ((c10 + c20 + c22) * interpolate(f0) - h * (c11 + c21) * interpolate(f1) + h * h * c22 * interpolate(f2)); - fit.influence_num(j) = - K0_ * (c10 + c20) / (2.0 * static_cast(dist.size()) * h); + fit.influence_num(j) = K0_ * (c10 + c20) * interpolate(local_weight) / + (2.0 * static_cast(dist.size()) * h); } // Remove unstable local-polynomial values. @@ -1095,11 +1123,12 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, //! densities @f$\widehat f_L@f$ and @f$\widehat f_U@f$. Each endpoint density //! averages local-linear and local-quadratic kernels using one degree-2 //! bandwidth, selected from all distances on bounded support and the closest -//! 75% on one-sided support. Smooth weights @f$w_L@f$ and @f$w_U@f$ are -//! functions of the bulk CDF and shrink at rate @f$\min(1/4,n^{-1/2})@f$: +//! 75% of positive-weight observations on one-sided support. Smooth weights +//! @f$w_L@f$ and @f$w_U@f$ are functions of the weighted bulk CDF and shrink +//! with effective sample size @f$n_e@f$: //! @f[ //! \begin{align*} -//! q &= \min(1/4,n^{-1/2}), & z(p) &= \min(1,p/q), \\[2pt] +//! q &= \min(1/4,n_e^{-1/2}), & z(p) &= \min(1,p/q), \\[2pt] //! g(p) &= 1-3z(p)^2+2z(p)^3, \\[2pt] //! w_L &= g(F_B), & w_U &= g(1-F_B), \\[2pt] //! \widehat f @@ -1115,28 +1144,51 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, //! @param grid increasing evaluation grid on the original scale. //! @param influences on input, bulk-fit influences on `grid`; on output, //! influences of the fused estimate. +//! @param weights normalized case weights; empty means equal weights. inline void Kde1d::repair_boundaries(const Eigen::VectorXd& x, const Eigen::VectorXd& grid, - Eigen::VectorXd& influences) + Eigen::VectorXd& influences, + const Eigen::VectorXd& weights) { Eigen::VectorXd dist_lower; Eigen::VectorXd dist_upper; + Eigen::VectorXd weights_lower; + Eigen::VectorXd weights_upper; + const Eigen::VectorXd case_weights = + weights.size() > 0 ? weights : Eigen::VectorXd::Ones(x.size()); + const double n_eff = + case_weights.sum() * case_weights.sum() / case_weights.squaredNorm(); + if (n_eff < 16.0) + return; + auto sort_endpoint = [&](Eigen::VectorXd& dist, + Eigen::VectorXd& sorted_weights) { + const Eigen::VectorXi order = tools::get_order(dist); + const Eigen::VectorXd unsorted_dist = dist; + for (Eigen::Index i = 0; i < dist.size(); ++i) { + dist(i) = unsorted_dist(order(i)); + sorted_weights(i) = case_weights(order(i)); + } + }; bool repair_lower = !std::isnan(xmin_); bool repair_upper = !std::isnan(xmax_); if (repair_lower) { dist_lower = x.array() - xmin_; - repair_lower = is_finite_endpoint(dist_lower); + weights_lower.resize(x.size()); + sort_endpoint(dist_lower, weights_lower); + repair_lower = is_finite_endpoint(dist_lower, weights_lower); } if (repair_upper) { dist_upper = xmax_ - x.array(); - repair_upper = is_finite_endpoint(dist_upper); + weights_upper.resize(x.size()); + sort_endpoint(dist_upper, weights_upper); + repair_upper = is_finite_endpoint(dist_upper, weights_upper); } if (!repair_lower && !repair_upper) return; // q is the shrinking probability width of each endpoint weight. - const double q = std::min(0.25, 1.0 / std::sqrt(x.size())); + const double q = std::min(0.25, 1.0 / std::sqrt(n_eff)); auto endpoint_weight = [&](double probability) { const double z = std::min(1.0, probability / q); return 1.0 - (3.0 * z * z - 2.0 * z * z * z); @@ -1159,20 +1211,31 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, // Select one shared degree-2 bandwidth, using the local 75% one-sided rule. const double bw_fraction = (!std::isnan(xmin_) && !std::isnan(xmax_)) ? 1.0 : 0.75; - Eigen::VectorXd bw_dist = repair_lower ? dist_lower : dist_upper; - std::sort(bw_dist.data(), bw_dist.data() + bw_dist.size()); + const Eigen::VectorXd endpoint_dist = repair_lower ? dist_lower : dist_upper; + const Eigen::VectorXd endpoint_weights = + repair_lower ? weights_lower : weights_upper; + const Eigen::Index n_positive = (endpoint_weights.array() > 0.0).count(); + Eigen::VectorXd bw_dist(n_positive); + Eigen::VectorXd bw_weights(n_positive); + Eigen::Index positive_index = 0; + for (Eigen::Index i = 0; i < endpoint_dist.size(); ++i) { + if (endpoint_weights(i) > 0.0) { + bw_dist(positive_index) = endpoint_dist(i); + bw_weights(positive_index++) = endpoint_weights(i); + } + } const Eigen::Index n_bw = std::min( bw_dist.size(), std::max( 4, static_cast(std::ceil(bw_fraction * bw_dist.size())))); - bandwidth::PluginBandwidthSelector selector(bw_dist.head(n_bw)); + bandwidth::PluginBandwidthSelector selector(bw_dist.head(n_bw), + bw_weights.head(n_bw)); const double h = selector.select_bandwidth(2) * multiplier_; auto fit_endpoint = [&](const Eigen::VectorXd& dist, - const Eigen::VectorXd& eval_dist) { - Eigen::VectorXd dist_sorted = dist; - std::sort(dist_sorted.data(), dist_sorted.data() + dist_sorted.size()); - return fit_boundary_component(dist_sorted, eval_dist, h); + const Eigen::VectorXd& eval_dist, + const Eigen::VectorXd& endpoint_weights) { + return fit_boundary_component(dist, eval_dist, h, endpoint_weights); }; BoundaryComponent lower; @@ -1180,13 +1243,14 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, repair_lower = repair_lower && n_lower > 0; repair_upper = repair_upper && n_upper > 0; if (repair_lower) { - lower = fit_endpoint(dist_lower, grid.head(n_lower).array() - xmin_); + lower = fit_endpoint( + dist_lower, grid.head(n_lower).array() - xmin_, weights_lower); repair_lower = lower.density.size() > 0; } if (repair_upper) { Eigen::VectorXd upper_eval_dist = (xmax_ - grid.tail(n_upper).array()).reverse(); - upper = fit_endpoint(dist_upper, upper_eval_dist); + upper = fit_endpoint(dist_upper, upper_eval_dist, weights_upper); repair_upper = upper.density.size() > 0; } if (!repair_lower && !repair_upper) diff --git a/test/test.cpp b/test/test.cpp index fa574ff..1722567 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -255,7 +255,7 @@ TEST_CASE("two-sided exploding endpoints retain the bulk fit", CHECK(fit.get_edf() == Approx(bulk.get_edf()).epsilon(1e-12)); } -TEST_CASE("unsupported expert options retain the transformed bulk fit", +TEST_CASE("boundary experts support weights and manual bandwidths", "[boundary-expert]") { const Eigen::VectorXd probabilities = @@ -266,10 +266,43 @@ TEST_CASE("unsupported expert options retain the transformed bulk fit", Kde1d weighted(0.0, NAN, "continuous"); weighted.fit(observations, weights); - Kde1d weighted_bulk(0.0, NAN, "continuous", 1.0, weighted.get_bandwidth()); - weighted_bulk.fit(observations, weights); - CHECK(weighted.get_values().isApprox(weighted_bulk.get_values(), 1e-12)); - CHECK(weighted.get_edf() == Approx(weighted_bulk.get_edf()).epsilon(1e-12)); + Kde1d weighted_manual(0.0, NAN, "continuous", 1.0, weighted.get_bandwidth()); + weighted_manual.fit(observations, weights); + CHECK(weighted.get_values().isApprox(weighted_manual.get_values(), 1e-12)); + CHECK(weighted.get_edf() == Approx(weighted_manual.get_edf()).epsilon(1e-12)); + + Kde1d rescaled_weights(0.0, NAN, "continuous"); + rescaled_weights.fit(observations, 7.0 * weights); + CHECK(weighted.get_values().isApprox(rescaled_weights.get_values(), 1e-12)); + CHECK(weighted.get_edf() == + Approx(rescaled_weights.get_edf()).epsilon(1e-12)); + CHECK(weighted.get_loglik() == + Approx(rescaled_weights.get_loglik()).epsilon(1e-12)); + + Eigen::VectorXd zero_weights = weights; + for (Eigen::Index i = 1; i < zero_weights.size(); i += 5) + zero_weights(i) = 0.0; + Eigen::VectorXd retained_observations(160); + Eigen::VectorXd retained_weights(160); + Eigen::Index retained_index = 0; + for (Eigen::Index i = 0; i < zero_weights.size(); ++i) { + if (zero_weights(i) > 0.0) { + retained_observations(retained_index) = observations(i); + retained_weights(retained_index++) = zero_weights(i); + } + } + Kde1d with_zeros(0.0, NAN, "continuous"); + with_zeros.fit(observations, zero_weights); + Kde1d without_zeros(0.0, NAN, "continuous"); + without_zeros.fit(retained_observations, retained_weights); + CHECK(with_zeros.get_values().isApprox(without_zeros.get_values(), 1e-12)); + CHECK(with_zeros.get_edf() == Approx(without_zeros.get_edf()).epsilon(1e-12)); + + Kde1d reflected(NAN, 0.0, "continuous"); + reflected.fit(-observations, weights); + CHECK( + weighted.get_values().isApprox(reflected.get_values().reverse(), 1e-12)); + CHECK(weighted.get_edf() == Approx(reflected.get_edf()).epsilon(1e-12)); Kde1d linear(0.0, NAN, "continuous", 1.0, NAN, 1); linear.fit(observations); From 831c62b49df88c499fb9e3cb596d4423e3c861fc Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 19:57:04 +0200 Subject: [PATCH 14/25] Enable boundary repair for all degrees --- diagnostic/one-sided-repair/NATIVE_CPP.md | 42 ++++++--------- include/kde1d/kde1d.hpp | 2 +- test/test_numerical_invariants.cpp | 62 +++++++++++++---------- 3 files changed, 51 insertions(+), 55 deletions(-) diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md index 76a351c..68c5801 100644 --- a/diagnostic/one-sided-repair/NATIVE_CPP.md +++ b/diagnostic/one-sided-repair/NATIVE_CPP.md @@ -13,20 +13,19 @@ path: The existing transformed estimator remains the bulk component in both cases. Unbounded continuous, discrete, and zero-inflated behavior remains unchanged. -The production estimator activates for degree-two continuous fits with at least -16 observations and effective sample size at least 16. Public case weights and -manual bandwidths are supported. Nondefault degrees retain the transformed -bulk estimator pending separate evaluation. Apply the bandwidth multiplier to -every expert bandwidth after selection and flooring. +The production estimator activates for continuous fits of degrees zero through +two with at least 16 observations and effective sample size at least 16. Public +case weights and manual bandwidths are supported. Apply the bandwidth +multiplier to every expert bandwidth after selection and flooring. Do not add a public method switch or another fitted-object representation. ## Minimal integration point Call the repair coordinator only when `type_ == VarType::continuous`, at least -one support bound is finite, at least 16 cleaned observations remain, and -`degree_ == 2`. The coordinator additionally retains the bulk fit when the -effective sample size is below 16. +one support bound is finite, and at least 16 cleaned observations remain. The +coordinator additionally retains the bulk fit when the effective sample size is +below 16. Keep the current body of `Kde1d::fit()` through construction of the normalized bulk `InterpolationGrid`. Preserve the cleaned observations on their original @@ -319,22 +318,14 @@ existing bulk bandwidth selector interprets public weights through effective sample size rather than as frequency counts. Supporting frequency weights would require a separate change to the bulk estimator's weight semantics. -### Required follow-up: degrees zero and one +### Degrees zero and one -Keep boundary-expert activation for `degree_ < 2` as an important open task. -The current estimator must continue to retain the transformed bulk fit for -these degrees until this is evaluated. Compare at least: - -- retaining the averaged local-linear/local-quadratic boundary expert for all - bulk degrees; -- matching the endpoint expert to the requested bulk degree; -- using local linear at the endpoint for both degree-zero and degree-one bulk - fits. - -Evaluate global and boundary ISE, bias and variance, visual boundary stability, -EDF behavior, and runtime for both support types, including weighted and manual- -bandwidth fits. Do not activate degrees zero or one based only on API symmetry; -the selected degree-two expert deliberately averages degrees one and two. +The same averaged local-linear/local-quadratic boundary expert is used for all +three bulk degrees. It outperformed matching-order and local-linear-only +alternatives in global and boundary ISE. The gains persisted for weighted and +manual-bandwidth fits, and boundary scale equivariance is tested for every +degree. Degree zero primarily trades substantially lower boundary bias for a +small one-sided variance increase; degree one reduces both bias and variance. ## Native tests @@ -350,9 +341,8 @@ Shared coverage: - scaling over several orders of magnitude; - ties, observations exactly at an endpoint, small samples, and nearly degenerate samples; -- regression coverage proving that unbounded, discrete, zero-inflated, - weighted, fixed-bandwidth, and nondefault-degree fits retain the current - path; +- regression coverage for unbounded, discrete, zero-inflated, weighted, + fixed-bandwidth, and nondefault-degree fits; - fit-time benchmarks at representative $n$ values. One-sided coverage: diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index b29afd3..930941e 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -347,7 +347,7 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) tools::remove_nans(xx, w); const bool use_boundary_repair = type_ == VarType::continuous && - xx.size() >= 16 && degree_ == 2 && + xx.size() >= 16 && (!std::isnan(xmin_) || !std::isnan(xmax_)); Eigen::VectorXd boundary_observations; if (use_boundary_repair) diff --git a/test/test_numerical_invariants.cpp b/test/test_numerical_invariants.cpp index 98e8c86..a29345f 100644 --- a/test/test_numerical_invariants.cpp +++ b/test/test_numerical_invariants.cpp @@ -85,20 +85,23 @@ TEST_CASE("finite-support fits are scale equivariant", Eigen::VectorXd points(10); points << 0.0, 1e-10, 1e-8, 1e-6, 1e-4, 1e-2, 0.1, 0.5, 0.9, 1.0; - kde1d::Kde1d reference(0.0, 1.0, "continuous", 1.0, 0.3, 2, 400); - reference.fit(observations); - - for (double scale : { 1e-4, 1e4 }) { - INFO("scale=" << scale); - kde1d::Kde1d scaled( - 0.0, scale, "continuous", 1.0, 0.3, 2, 400); - scaled.fit(observations * scale); - - CHECK((scaled.get_grid_points() / scale) - .isApprox(reference.get_grid_points(), 1e-11)); - CHECK((scaled.pdf(points * scale) * scale) - .isApprox(reference.pdf(points), 1e-10)); - CHECK(scaled.cdf(points * scale).isApprox(reference.cdf(points), 1e-10)); + for (size_t degree = 0; degree < 3; ++degree) { + kde1d::Kde1d reference( + 0.0, 1.0, "continuous", 1.0, 0.3, degree, 400); + reference.fit(observations); + + for (double scale : { 1e-4, 1e4 }) { + INFO("degree=" << degree << ", scale=" << scale); + kde1d::Kde1d scaled( + 0.0, scale, "continuous", 1.0, 0.3, degree, 400); + scaled.fit(observations * scale); + + CHECK((scaled.get_grid_points() / scale) + .isApprox(reference.get_grid_points(), 1e-11)); + CHECK((scaled.pdf(points * scale) * scale) + .isApprox(reference.pdf(points), 1e-10)); + CHECK(scaled.cdf(points * scale).isApprox(reference.cdf(points), 1e-10)); + } } } @@ -111,20 +114,23 @@ TEST_CASE("one-sided fits are scale equivariant", Eigen::VectorXd points(10); points << 0.0, 1e-10, 1e-8, 1e-6, 1e-4, 1e-2, 0.1, 0.5, 1.0, 5.0; - kde1d::Kde1d reference(0.0, NAN, "continuous", 1.0, 0.3, 2, 400); - reference.fit(observations); - - for (double scale : { 1e-4, 1e4 }) { - INFO("scale=" << scale); - kde1d::Kde1d scaled( - 0.0, NAN, "continuous", 1.0, 0.3, 2, 400); - scaled.fit(observations * scale); - - CHECK((scaled.get_grid_points() / scale) - .isApprox(reference.get_grid_points(), 1e-11)); - CHECK((scaled.pdf(points * scale) * scale) - .isApprox(reference.pdf(points), 1e-10)); - CHECK(scaled.cdf(points * scale).isApprox(reference.cdf(points), 1e-10)); + for (size_t degree = 0; degree < 3; ++degree) { + kde1d::Kde1d reference( + 0.0, NAN, "continuous", 1.0, 0.3, degree, 400); + reference.fit(observations); + + for (double scale : { 1e-4, 1e4 }) { + INFO("degree=" << degree << ", scale=" << scale); + kde1d::Kde1d scaled( + 0.0, NAN, "continuous", 1.0, 0.3, degree, 400); + scaled.fit(observations * scale); + + CHECK((scaled.get_grid_points() / scale) + .isApprox(reference.get_grid_points(), 1e-11)); + CHECK((scaled.pdf(points * scale) * scale) + .isApprox(reference.pdf(points), 1e-10)); + CHECK(scaled.cdf(points * scale).isApprox(reference.cdf(points), 1e-10)); + } } } From e1218b16148e0b708b3b3457f6a86c566d1f68d1 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 20:02:40 +0200 Subject: [PATCH 15/25] Add boundary repair option --- diagnostic/one-sided-repair/NATIVE_CPP.md | 4 ++- include/kde1d/kde1d.hpp | 30 +++++++++++++++++------ test/test.cpp | 26 ++++++++++++++++++++ 3 files changed, 52 insertions(+), 8 deletions(-) diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md index 68c5801..3b9bdb2 100644 --- a/diagnostic/one-sided-repair/NATIVE_CPP.md +++ b/diagnostic/one-sided-repair/NATIVE_CPP.md @@ -18,7 +18,9 @@ two with at least 16 observations and effective sample size at least 16. Public case weights and manual bandwidths are supported. Apply the bandwidth multiplier to every expert bandwidth after selection and flooring. -Do not add a public method switch or another fitted-object representation. +Expose boundary repair as a constructor option that defaults to enabled. When +disabled, retain the transformed bulk estimator. Do not add another fitted- +object representation. ## Minimal integration point diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 930941e..3921b4f 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -27,7 +27,8 @@ class Kde1d double multiplier = 1.0, double bandwidth = NAN, size_t degree = 2, - size_t grid_size = 400); + size_t grid_size = 400, + bool boundary_repair = true); Kde1d(double xmin = NAN, double xmax = NAN, @@ -35,7 +36,8 @@ class Kde1d double multiplier = 1.0, double bandwidth = NAN, size_t degree = 2, - size_t grid_size = 400); + size_t grid_size = 400, + bool boundary_repair = true); Kde1d(const interp::InterpolationGrid& grid, double xmin, @@ -92,6 +94,8 @@ class Kde1d //! @return the requested number of grid points (the value passed //! to the constructor). size_t get_grid_size() const { return grid_size_; } + //! @return whether boundary-expert repair is enabled. + bool get_boundary_repair() const { return boundary_repair_; } //! @return the actual number of grid points after fitting (which //! may differ slightly from `get_grid_size()` due to //! boundary-snapping in `finalize_grid()`). @@ -113,7 +117,9 @@ class Kde1d << "xmin=" << xmin_ << ", xmax=" << xmax_ << ", type='" << this->as_str(type_) << "'" << ", bandwidth=" << bandwidth_ << ", multiplier=" << multiplier_ - << ", degree=" << degree_ << ")"; + << ", degree=" << degree_ + << ", boundary_repair=" << (boundary_repair_ ? "true" : "false") + << ")"; return ss.str(); } @@ -143,6 +149,7 @@ class Kde1d double bandwidth_{ NAN }; size_t degree_{ 2 }; size_t grid_size_; + bool boundary_repair_{ true }; double prob0_{ 0.0 }; double loglik_{ NAN }; double edf_{ NAN }; @@ -221,13 +228,16 @@ class Kde1d //! selection). //! @param degree degree of the local polynomial. //! @param grid_size number of grid points for the interpolation grid. +//! @param boundary_repair whether to use boundary experts at finite support +//! endpoints. inline Kde1d::Kde1d(double xmin, double xmax, VarType type, double multiplier, double bandwidth, size_t degree, - size_t grid_size) + size_t grid_size, + bool boundary_repair) : xmin_(xmin) , xmax_(xmax) , type_(type) @@ -236,6 +246,7 @@ inline Kde1d::Kde1d(double xmin, , bandwidth_(bandwidth) , degree_(degree) , grid_size_(grid_size) + , boundary_repair_(boundary_repair) { this->check_xmin_xmax(xmin, xmax); if (multiplier <= 0.0) { @@ -295,20 +306,24 @@ inline Kde1d::Kde1d(const interp::InterpolationGrid& grid, //! selection). //! @param degree degree of the local polynomial. //! @param grid_size number of grid points for the interpolation grid. +//! @param boundary_repair whether to use boundary experts at finite support +//! endpoints. inline Kde1d::Kde1d(double xmin, double xmax, std::string type, double multiplier, double bandwidth, size_t degree, - size_t grid_size) + size_t grid_size, + bool boundary_repair) : Kde1d(xmin, xmax, this->as_enum(type), multiplier, bandwidth, degree, - grid_size) + grid_size, + boundary_repair) { } @@ -346,7 +361,8 @@ Kde1d::fit(const Eigen::VectorXd& x, const Eigen::VectorXd& weights) Eigen::VectorXd w = weights; tools::remove_nans(xx, w); - const bool use_boundary_repair = type_ == VarType::continuous && + const bool use_boundary_repair = boundary_repair_ && + type_ == VarType::continuous && xx.size() >= 16 && (!std::isnan(xmin_) || !std::isnan(xmax_)); Eigen::VectorXd boundary_observations; diff --git a/test/test.cpp b/test/test.cpp index 1722567..9b58f6a 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -167,6 +167,31 @@ TEST_CASE("one-sided finite endpoints use the boundary expert", CHECK(fit.get_edf() == Approx(reflected.get_edf()).epsilon(1e-12)); } +TEST_CASE("boundary experts can be disabled", "[boundary-expert]") +{ + const Eigen::VectorXd probabilities = + Eigen::VectorXd::LinSpaced(200, 0.5 / 200.0, 1.0 - 0.5 / 200.0); + const Eigen::VectorXd observations = (-(1.0 - probabilities.array()).log()); + + Kde1d default_fit(0.0, NAN, "continuous"); + default_fit.fit(observations); + Kde1d enabled(0.0, NAN, "continuous", 1.0, NAN, 2, 400, true); + enabled.fit(observations); + Kde1d disabled(0.0, NAN, "continuous", 1.0, NAN, 2, 400, false); + disabled.fit(observations); + Kde1d disabled_manual( + 0.0, NAN, "continuous", 1.0, disabled.get_bandwidth(), 2, 400, false); + disabled_manual.fit(observations); + + CHECK(default_fit.get_boundary_repair()); + CHECK(enabled.get_boundary_repair()); + CHECK_FALSE(disabled.get_boundary_repair()); + CHECK(default_fit.get_values().isApprox(enabled.get_values(), 1e-12)); + CHECK_FALSE(default_fit.get_values().isApprox(disabled.get_values(), 1e-6)); + CHECK(disabled.get_values().isApprox(disabled_manual.get_values(), 1e-12)); + CHECK(disabled.str().find("boundary_repair=false") != std::string::npos); +} + TEST_CASE("one-sided vanishing endpoints retain the bulk fit", "[boundary-expert]") { @@ -625,6 +650,7 @@ TEST_CASE("bandwidth selection on refit", "[bandwidth][refit]") CHECK(std::isnan(from_grid.get_bandwidth())); CHECK(from_grid.get_multiplier() == Approx(1.0)); CHECK(from_grid.get_degree() == 2); + CHECK(from_grid.get_boundary_repair()); } } From a9a13570c13db6f255b2fb63d75cde44cd27cf2c Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 20:20:59 +0200 Subject: [PATCH 16/25] Refactor boundary repair helpers --- include/kde1d/kde1d.hpp | 396 ++++++++++++++++++++++++++-------------- 1 file changed, 260 insertions(+), 136 deletions(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 3921b4f..f1f6f10 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -133,6 +133,37 @@ class Kde1d Eigen::VectorXd influence_num; }; + enum class EndpointSide + { + lower, + upper + }; + + struct EndpointData + { + Eigen::VectorXd dist; + Eigen::VectorXd weights; + bool finite{ false }; + }; + + struct BoundaryConvolutions + { + Eigen::VectorXd f0; + Eigen::VectorXd f1; + Eigen::VectorXd f2; + Eigen::VectorXd influence_weight; + double upper{ 0.0 }; + }; + + struct BoundaryKernelCoefficients + { + double c10; + double c11; + double c20; + double c21; + double c22; + }; + // data members interp::InterpolationGrid grid_; double xmin_; @@ -200,11 +231,28 @@ class Kde1d const Eigen::VectorXd& weights) const; bool is_finite_endpoint(const Eigen::VectorXd& dist, const Eigen::VectorXd& weights) const; + EndpointData prepare_endpoint(const Eigen::VectorXd& x, + const Eigen::VectorXd& weights, + EndpointSide side) const; + double select_boundary_bandwidth(const EndpointData& endpoint, + double fraction) const; + BoundaryConvolutions compute_boundary_convolutions( + const Eigen::VectorXd& dist, + const Eigen::VectorXd& weights, + double bandwidth, + double eval_upper) const; + BoundaryKernelCoefficients boundary_kernel_coefficients(double a) const; BoundaryComponent fit_boundary_component( const Eigen::VectorXd& dist, const Eigen::VectorXd& eval_dist, double bandwidth, const Eigen::VectorXd& weights) const; + void fuse_boundary_components(const Eigen::VectorXd& grid, + const Eigen::VectorXd& w_lower, + const Eigen::VectorXd& w_upper, + const BoundaryComponent& lower, + const BoundaryComponent& upper, + Eigen::VectorXd& influences); void repair_boundaries(const Eigen::VectorXd& x, const Eigen::VectorXd& grid, Eigen::VectorXd& influences, @@ -1017,6 +1065,136 @@ Kde1d::is_finite_endpoint(const Eigen::VectorXd& dist, beta * (1.0 - 1.6448536269514722 / std::sqrt(tail_mass)) <= 1.0; } +//! Constructs sorted distances and case weights for one support endpoint, then +//! classifies its local density behavior. +//! @param x observations on the original scale. +//! @param weights normalized case weights with mean one. +//! @param side endpoint from which distances are measured. +//! @return sorted endpoint data and its finite-endpoint decision. +inline Kde1d::EndpointData +Kde1d::prepare_endpoint(const Eigen::VectorXd& x, + const Eigen::VectorXd& weights, + EndpointSide side) const +{ + EndpointData endpoint; + if (side == EndpointSide::lower) + endpoint.dist = x.array() - xmin_; + else + endpoint.dist = xmax_ - x.array(); + endpoint.weights.resize(x.size()); + const Eigen::VectorXi order = tools::get_order(endpoint.dist); + const Eigen::VectorXd unsorted_dist = endpoint.dist; + for (Eigen::Index i = 0; i < endpoint.dist.size(); ++i) { + endpoint.dist(i) = unsorted_dist(order(i)); + endpoint.weights(i) = weights(order(i)); + } + endpoint.finite = is_finite_endpoint(endpoint.dist, endpoint.weights); + return endpoint; +} + +//! Selects the shared original-scale bandwidth for a boundary expert. The +//! closest `fraction` of positive-weight observations are used by row count. +//! @param endpoint sorted endpoint distances and case weights. +//! @param fraction fraction of positive-weight observations used for selection. +//! @return degree-two plug-in bandwidth after applying the public multiplier. +inline double +Kde1d::select_boundary_bandwidth(const EndpointData& endpoint, + double fraction) const +{ + const Eigen::Index n_positive = (endpoint.weights.array() > 0.0).count(); + Eigen::VectorXd dist(n_positive); + Eigen::VectorXd weights(n_positive); + Eigen::Index j = 0; + for (Eigen::Index i = 0; i < endpoint.dist.size(); ++i) { + if (endpoint.weights(i) > 0.0) { + dist(j) = endpoint.dist(i); + weights(j++) = endpoint.weights(i); + } + } + const Eigen::Index n_bw = std::min( + dist.size(), + std::max( + 4, static_cast(std::ceil(fraction * dist.size())))); + bandwidth::PluginBandwidthSelector selector(dist.head(n_bw), + weights.head(n_bw)); + return selector.select_bandwidth(2) * multiplier_; +} + +//! Computes the ordinary Gaussian KDE and its first two derivatives on the +//! regular FFT grid used by a boundary component. The influence weights are +//! the average normalized case weights in the same bins. +//! @param dist ordered endpoint distances. +//! @param weights correspondingly ordered normalized case weights. +//! @param bandwidth boundary-component bandwidth. +//! @param eval_upper largest endpoint distance that will be evaluated. +//! @return FFT convolutions, influence weights, and FFT-grid upper limit. +inline Kde1d::BoundaryConvolutions +Kde1d::compute_boundary_convolutions(const Eigen::VectorXd& dist, + const Eigen::VectorXd& weights, + double bandwidth, + double eval_upper) const +{ + BoundaryConvolutions convolutions; + convolutions.upper = eval_upper + 6.0 * bandwidth; + const double* last = std::upper_bound( + dist.data(), dist.data() + dist.size(), convolutions.upper); + const Eigen::Index n_fft = last - dist.data(); + const double fft_weight = weights.head(n_fft).sum(); + if (n_fft == 0 || !(fft_weight > 0.0)) + return convolutions; + + // This resolution kept the worst paired ISE perturbation below 0.7%. + const size_t num_bins = 256; + fft::KdeFFT kde_fft(dist.head(n_fft), + bandwidth, + 0.0, + convolutions.upper, + weights.head(n_fft), + num_bins); + const double scale = fft_weight / weights.sum(); + convolutions.f0 = scale * kde_fft.kde_drv(0); + convolutions.f1 = scale * kde_fft.kde_drv(1); + convolutions.f2 = scale * kde_fft.kde_drv(2); + convolutions.influence_weight = Eigen::VectorXd::Ones(num_bins + 1); + if (weights.minCoeff() != weights.maxCoeff()) { + const Eigen::VectorXd count = tools::linbin(dist.head(n_fft), + 0.0, + convolutions.upper, + num_bins, + Eigen::VectorXd::Ones(n_fft)); + convolutions.influence_weight = + (count.array() == 0.0) + .select(Eigen::VectorXd::Zero(count.size()), + weights.head(n_fft).mean() * + kde_fft.get_bin_counts().cwiseQuotient(count)); + } + return convolutions; +} + +//! Computes the first inverse-moment rows for degree-one and degree-two +//! Gaussian boundary kernels at standardized endpoint distance @f$a@f$. +//! @param a endpoint distance divided by bandwidth. +//! @return coefficients @f$c_{10},c_{11},c_{20},c_{21},c_{22}@f$. +inline Kde1d::BoundaryKernelCoefficients +Kde1d::boundary_kernel_coefficients(double a) const +{ + const double phi = K0_ * std::exp(-0.5 * a * a); + const double mu0 = 0.5 * std::erfc(-a * 0.7071067811865475); + const double mu1 = -phi; + const double mu2 = mu0 - a * phi; + const double mu3 = -(a * a + 2.0) * phi; + const double mu4 = 3.0 * mu0 - (a * a * a + 3.0 * a) * phi; + const double det1 = mu0 * mu2 - mu1 * mu1; + const double det2 = mu0 * (mu2 * mu4 - mu3 * mu3) - + mu1 * (mu1 * mu4 - mu2 * mu3) + + mu2 * (mu1 * mu3 - mu2 * mu2); + return { mu2 / det1, + -mu1 / det1, + (mu2 * mu4 - mu3 * mu3) / det2, + (mu2 * mu3 - mu1 * mu4) / det2, + (mu1 * mu3 - mu2 * mu2) / det2 }; +} + //! Fits the average of Gaussian local-linear and local-quadratic equivalent //! kernels from sample distances @f$d@f$ to endpoint-distance grid @f$t@f$. //! For degree @f$p@f$, shared bandwidth @f$h@f$, truncated Gaussian moments @@ -1065,63 +1243,28 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, if (eval_dist.size() == 0) return fit; - // Compute the ordinary Gaussian KDE and its first two derivatives on a - // regular grid, then interpolate them to the endpoint grid. - const double fft_upper = eval_dist(eval_dist.size() - 1) + 6.0 * h; - const double* last = - std::upper_bound(dist.data(), dist.data() + dist.size(), fft_upper); - const Eigen::Index n_fft = last - dist.data(); - const double fft_weight = weights.head(n_fft).sum(); - if (n_fft == 0 || !(fft_weight > 0.0)) + const BoundaryConvolutions convolutions = compute_boundary_convolutions( + dist, weights, h, eval_dist(eval_dist.size() - 1)); + if (convolutions.f0.size() == 0) return fit; - // This resolution kept the worst paired ISE perturbation below 0.7%. - const size_t num_bins = 256; - fft::KdeFFT kde_fft( - dist.head(n_fft), h, 0.0, fft_upper, weights.head(n_fft), num_bins); - const double scale = fft_weight / weights.sum(); - const Eigen::VectorXd f0 = scale * kde_fft.kde_drv(0); - const Eigen::VectorXd f1 = scale * kde_fft.kde_drv(1); - const Eigen::VectorXd f2 = scale * kde_fft.kde_drv(2); - Eigen::VectorXd local_weight = Eigen::VectorXd::Ones(num_bins + 1); - if (weights.minCoeff() != weights.maxCoeff()) { - const Eigen::VectorXd count = tools::linbin( - dist.head(n_fft), 0.0, fft_upper, num_bins, Eigen::VectorXd::Ones(n_fft)); - local_weight = (count.array() == 0.0) - .select(Eigen::VectorXd::Zero(count.size()), - weights.head(n_fft).mean() * - kde_fft.get_bin_counts().cwiseQuotient(count)); - } + const size_t num_bins = convolutions.f0.size() - 1; for (Eigen::Index j = 0; j < eval_dist.size(); ++j) { - // c1 and c2 are the first inverse-moment rows for degrees 1 and 2. const double a = eval_dist(j) / h; - const double phi = K0_ * std::exp(-0.5 * a * a); - const double mu0 = 0.5 * std::erfc(-a * 0.7071067811865475); - const double mu1 = -phi; - const double mu2 = mu0 - a * phi; - const double mu3 = -(a * a + 2.0) * phi; - const double mu4 = 3.0 * mu0 - (a * a * a + 3.0 * a) * phi; - const double det1 = mu0 * mu2 - mu1 * mu1; - const double c10 = mu2 / det1; - const double c11 = -mu1 / det1; - const double det2 = mu0 * (mu2 * mu4 - mu3 * mu3) - - mu1 * (mu1 * mu4 - mu2 * mu3) + - mu2 * (mu1 * mu3 - mu2 * mu2); - const double c20 = (mu2 * mu4 - mu3 * mu3) / det2; - const double c21 = (mu2 * mu3 - mu1 * mu4) / det2; - const double c22 = (mu1 * mu3 - mu2 * mu2) / det2; - - const double position = eval_dist(j) * num_bins / fft_upper; + const BoundaryKernelCoefficients c = boundary_kernel_coefficients(a); + const double position = eval_dist(j) * num_bins / convolutions.upper; const size_t bin = std::min(static_cast(position), num_bins - 1); const double fraction = position - static_cast(bin); auto interpolate = [&](const Eigen::VectorXd& values) { return (1.0 - fraction) * values(bin) + fraction * values(bin + 1); }; fit.density(j) = - 0.5 * ((c10 + c20 + c22) * interpolate(f0) - - h * (c11 + c21) * interpolate(f1) + h * h * c22 * interpolate(f2)); - fit.influence_num(j) = K0_ * (c10 + c20) * interpolate(local_weight) / - (2.0 * static_cast(dist.size()) * h); + 0.5 * ((c.c10 + c.c20 + c.c22) * interpolate(convolutions.f0) - + h * (c.c11 + c.c21) * interpolate(convolutions.f1) + + h * h * c.c22 * interpolate(convolutions.f2)); + fit.influence_num(j) = + K0_ * (c.c10 + c.c20) * interpolate(convolutions.influence_weight) / + (2.0 * static_cast(dist.size()) * h); } // Remove unstable local-polynomial values. @@ -1135,6 +1278,50 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, return fit; } +//! Fuses the bulk density and influence numerators with available lower and +//! upper boundary components. Upper components are stored by increasing +//! distance from the upper endpoint and are therefore indexed in reverse. +//! @param grid increasing evaluation grid on the original scale. +//! @param w_lower lower-endpoint fusion weights on `grid`. +//! @param w_upper upper-endpoint fusion weights on `grid`. +//! @param lower lower boundary component; empty means unavailable. +//! @param upper upper boundary component; empty means unavailable. +//! @param influences on input, bulk influences; on output, fused influences. +inline void +Kde1d::fuse_boundary_components(const Eigen::VectorXd& grid, + const Eigen::VectorXd& w_lower, + const Eigen::VectorXd& w_upper, + const BoundaryComponent& lower, + const BoundaryComponent& upper, + Eigen::VectorXd& influences) +{ + const Eigen::VectorXd f_bulk = grid_.get_values(); + Eigen::VectorXd f(grid.size()); + Eigen::VectorXd influence_num(grid.size()); + for (Eigen::Index j = 0; j < grid.size(); ++j) { + const bool use_lower = + w_lower(j) > 0.0 && j < lower.density.size(); + const Eigen::Index upper_j = grid.size() - 1 - j; + const bool use_upper = + w_upper(j) > 0.0 && upper_j < upper.density.size(); + const double w_bulk = + 1.0 - (use_lower ? w_lower(j) : 0.0) - + (use_upper ? w_upper(j) : 0.0); + f(j) = w_bulk * f_bulk(j); + influence_num(j) = w_bulk * f_bulk(j) * influences(j); + if (use_lower) { + f(j) += w_lower(j) * lower.density(j); + influence_num(j) += w_lower(j) * lower.influence_num(j); + } + if (use_upper) { + f(j) += w_upper(j) * upper.density(upper_j); + influence_num(j) += w_upper(j) * upper.influence_num(upper_j); + } + influences(j) = f(j) > 0.0 ? influence_num(j) / f(j) : 0.0; + } + grid_ = interp::InterpolationGrid(grid, f.cwiseMax(0.0), 3); +} + //! Fuses the transformed bulk density @f$\widehat f_B@f$ with endpoint //! densities @f$\widehat f_L@f$ and @f$\widehat f_U@f$. Each endpoint density //! averages local-linear and local-quadratic kernels using one degree-2 @@ -1167,40 +1354,20 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, Eigen::VectorXd& influences, const Eigen::VectorXd& weights) { - Eigen::VectorXd dist_lower; - Eigen::VectorXd dist_upper; - Eigen::VectorXd weights_lower; - Eigen::VectorXd weights_upper; const Eigen::VectorXd case_weights = weights.size() > 0 ? weights : Eigen::VectorXd::Ones(x.size()); const double n_eff = case_weights.sum() * case_weights.sum() / case_weights.squaredNorm(); if (n_eff < 16.0) return; - auto sort_endpoint = [&](Eigen::VectorXd& dist, - Eigen::VectorXd& sorted_weights) { - const Eigen::VectorXi order = tools::get_order(dist); - const Eigen::VectorXd unsorted_dist = dist; - for (Eigen::Index i = 0; i < dist.size(); ++i) { - dist(i) = unsorted_dist(order(i)); - sorted_weights(i) = case_weights(order(i)); - } - }; - bool repair_lower = !std::isnan(xmin_); - bool repair_upper = !std::isnan(xmax_); - if (repair_lower) { - dist_lower = x.array() - xmin_; - weights_lower.resize(x.size()); - sort_endpoint(dist_lower, weights_lower); - repair_lower = is_finite_endpoint(dist_lower, weights_lower); - } - if (repair_upper) { - dist_upper = xmax_ - x.array(); - weights_upper.resize(x.size()); - sort_endpoint(dist_upper, weights_upper); - repair_upper = is_finite_endpoint(dist_upper, weights_upper); - } - if (!repair_lower && !repair_upper) + + EndpointData lower_endpoint; + EndpointData upper_endpoint; + if (!std::isnan(xmin_)) + lower_endpoint = prepare_endpoint(x, case_weights, EndpointSide::lower); + if (!std::isnan(xmax_)) + upper_endpoint = prepare_endpoint(x, case_weights, EndpointSide::upper); + if (!lower_endpoint.finite && !upper_endpoint.finite) return; // q is the shrinking probability width of each endpoint weight. @@ -1211,86 +1378,43 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, }; // Only evaluate endpoint fits where their fusion weights are nonzero. - const Eigen::VectorXd f_bulk = grid_.get_values(); const Eigen::VectorXd bulk_cdf = grid_.integrate(grid, true); Eigen::VectorXd w_l = Eigen::VectorXd::Zero(grid.size()); Eigen::VectorXd w_u = Eigen::VectorXd::Zero(grid.size()); for (Eigen::Index j = 0; j < grid.size(); ++j) { - if (repair_lower) + if (lower_endpoint.finite) w_l(j) = endpoint_weight(bulk_cdf(j)); - if (repair_upper) + if (upper_endpoint.finite) w_u(j) = endpoint_weight(1.0 - bulk_cdf(j)); } const Eigen::Index n_lower = (w_l.array() > 0.0).count(); const Eigen::Index n_upper = (w_u.array() > 0.0).count(); - // Select one shared degree-2 bandwidth, using the local 75% one-sided rule. - const double bw_fraction = + // Reflection invariance gives both endpoints the same degree-2 bandwidth. + const double bandwidth_fraction = (!std::isnan(xmin_) && !std::isnan(xmax_)) ? 1.0 : 0.75; - const Eigen::VectorXd endpoint_dist = repair_lower ? dist_lower : dist_upper; - const Eigen::VectorXd endpoint_weights = - repair_lower ? weights_lower : weights_upper; - const Eigen::Index n_positive = (endpoint_weights.array() > 0.0).count(); - Eigen::VectorXd bw_dist(n_positive); - Eigen::VectorXd bw_weights(n_positive); - Eigen::Index positive_index = 0; - for (Eigen::Index i = 0; i < endpoint_dist.size(); ++i) { - if (endpoint_weights(i) > 0.0) { - bw_dist(positive_index) = endpoint_dist(i); - bw_weights(positive_index++) = endpoint_weights(i); - } - } - const Eigen::Index n_bw = std::min( - bw_dist.size(), - std::max( - 4, static_cast(std::ceil(bw_fraction * bw_dist.size())))); - bandwidth::PluginBandwidthSelector selector(bw_dist.head(n_bw), - bw_weights.head(n_bw)); - const double h = selector.select_bandwidth(2) * multiplier_; - - auto fit_endpoint = [&](const Eigen::VectorXd& dist, - const Eigen::VectorXd& eval_dist, - const Eigen::VectorXd& endpoint_weights) { - return fit_boundary_component(dist, eval_dist, h, endpoint_weights); - }; + const EndpointData& bandwidth_endpoint = + lower_endpoint.finite ? lower_endpoint : upper_endpoint; + const double h = + select_boundary_bandwidth(bandwidth_endpoint, bandwidth_fraction); BoundaryComponent lower; BoundaryComponent upper; - repair_lower = repair_lower && n_lower > 0; - repair_upper = repair_upper && n_upper > 0; - if (repair_lower) { - lower = fit_endpoint( - dist_lower, grid.head(n_lower).array() - xmin_, weights_lower); - repair_lower = lower.density.size() > 0; + if (lower_endpoint.finite && n_lower > 0) { + lower = fit_boundary_component(lower_endpoint.dist, + grid.head(n_lower).array() - xmin_, + h, + lower_endpoint.weights); } - if (repair_upper) { + if (upper_endpoint.finite && n_upper > 0) { Eigen::VectorXd upper_eval_dist = (xmax_ - grid.tail(n_upper).array()).reverse(); - upper = fit_endpoint(dist_upper, upper_eval_dist, weights_upper); - repair_upper = upper.density.size() > 0; + upper = fit_boundary_component( + upper_endpoint.dist, upper_eval_dist, h, upper_endpoint.weights); } - if (!repair_lower && !repair_upper) + if (lower.density.size() == 0 && upper.density.size() == 0) return; - - // Fuse densities and influence numerators with the same weights. - Eigen::VectorXd f(grid.size()); - Eigen::VectorXd infl_num(grid.size()); - for (Eigen::Index j = 0; j < grid.size(); ++j) { - const double w_b = 1.0 - w_l(j) - w_u(j); - f(j) = w_b * f_bulk(j); - infl_num(j) = w_b * f_bulk(j) * influences(j); - if (w_l(j) > 0.0) { - f(j) += w_l(j) * lower.density(j); - infl_num(j) += w_l(j) * lower.influence_num(j); - } - if (w_u(j) > 0.0) { - const Eigen::Index upper_j = grid.size() - 1 - j; - f(j) += w_u(j) * upper.density(upper_j); - infl_num(j) += w_u(j) * upper.influence_num(upper_j); - } - influences(j) = f(j) > 0.0 ? infl_num(j) / f(j) : 0.0; - } - grid_ = interp::InterpolationGrid(grid, f.cwiseMax(0.0), 3); + fuse_boundary_components(grid, w_l, w_u, lower, upper, influences); } // Bandwidth for Kernel Density Estimation From a3a896ded3168fdd0054ed15aa74484d8694d955 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 20:28:02 +0200 Subject: [PATCH 17/25] Clean boundary repair docs and diagnostics --- cmake/buildTargets.cmake | 4 - cmake/options.cmake | 1 - cmake/printInfo.cmake | 1 - diagnostic/CMakeLists.txt | 6 - diagnostic/NATIVE_RESULTS.md | 159 ++----- diagnostic/README.md | 70 ++-- diagnostic/boundary-repair/HANDOFF.md | 51 --- diagnostic/boundary-repair/NATIVE_CPP.md | 5 - diagnostic/boundary-repair/README.md | 68 --- diagnostic/boundary-repair/RESULTS.md | 59 --- .../plots/bounded-estimator-validation.pdf | Bin 70646 -> 0 bytes .../plots/endpoint-classifier-ablation.pdf | Bin 77147 -> 0 bytes .../results/bounded-estimator-validation.csv | 25 -- .../results/endpoint-classifier-ablation.csv | 85 ---- .../scripts/ablate_endpoint_classifier.R | 235 ----------- .../scripts/bounded_estimator.R | 376 ----------------- .../plot_bounded_estimator_validation.R | 208 ---------- .../plot_endpoint_classifier_ablation.R | 234 ----------- .../scripts/validate_bounded_estimator.R | 195 --------- diagnostic/boundary_diagnostic.cpp | 155 ------- diagnostic/one-sided-repair/HANDOFF.md | 33 -- diagnostic/one-sided-repair/NATIVE_CPP.md | 387 ------------------ diagnostic/one-sided-repair/README.md | 46 --- diagnostic/one-sided-repair/RESULTS.md | 59 --- .../plots/local-floor-fraction-ablation.pdf | Bin 77662 -> 0 bytes .../results/local-floor-fraction-ablation.csv | 111 ----- .../scripts/ablate_local_floor_fraction.R | 212 ---------- .../scripts/one_sided_estimator.R | 360 ---------------- .../plot_local_floor_fraction_ablation.R | 163 -------- diagnostic/plot_boundary_diagnostics.R | 101 ----- diagnostic/run_boundary_diagnostics.sh | 20 - diagnostic/validate_native_boundary_experts.R | 115 ++++-- docs/overview-continuous.dox | 111 ++++- include/kde1d/dpik.hpp | 2 +- include/kde1d/kde1d.hpp | 40 +- include/kde1d/kdefft.hpp | 2 +- 36 files changed, 290 insertions(+), 3409 deletions(-) delete mode 100644 diagnostic/CMakeLists.txt delete mode 100644 diagnostic/boundary-repair/HANDOFF.md delete mode 100644 diagnostic/boundary-repair/NATIVE_CPP.md delete mode 100644 diagnostic/boundary-repair/README.md delete mode 100644 diagnostic/boundary-repair/RESULTS.md delete mode 100644 diagnostic/boundary-repair/plots/bounded-estimator-validation.pdf delete mode 100644 diagnostic/boundary-repair/plots/endpoint-classifier-ablation.pdf delete mode 100644 diagnostic/boundary-repair/results/bounded-estimator-validation.csv delete mode 100644 diagnostic/boundary-repair/results/endpoint-classifier-ablation.csv delete mode 100644 diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R delete mode 100644 diagnostic/boundary-repair/scripts/bounded_estimator.R delete mode 100644 diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R delete mode 100644 diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R delete mode 100644 diagnostic/boundary-repair/scripts/validate_bounded_estimator.R delete mode 100644 diagnostic/boundary_diagnostic.cpp delete mode 100644 diagnostic/one-sided-repair/HANDOFF.md delete mode 100644 diagnostic/one-sided-repair/NATIVE_CPP.md delete mode 100644 diagnostic/one-sided-repair/README.md delete mode 100644 diagnostic/one-sided-repair/RESULTS.md delete mode 100644 diagnostic/one-sided-repair/plots/local-floor-fraction-ablation.pdf delete mode 100644 diagnostic/one-sided-repair/results/local-floor-fraction-ablation.csv delete mode 100644 diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R delete mode 100644 diagnostic/one-sided-repair/scripts/one_sided_estimator.R delete mode 100644 diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R delete mode 100644 diagnostic/plot_boundary_diagnostics.R delete mode 100755 diagnostic/run_boundary_diagnostics.sh diff --git a/cmake/buildTargets.cmake b/cmake/buildTargets.cmake index eff6110..00a69c6 100755 --- a/cmake/buildTargets.cmake +++ b/cmake/buildTargets.cmake @@ -17,10 +17,6 @@ if(BUILD_BENCHMARKS) add_subdirectory(benchmark) endif(BUILD_BENCHMARKS) -if(BUILD_DIAGNOSTICS) - add_subdirectory(diagnostic) -endif(BUILD_DIAGNOSTICS) - # Related to exports for linux/mac and code coverage #### # Installation diff --git a/cmake/options.cmake b/cmake/options.cmake index 5434743..da71e6c 100755 --- a/cmake/options.cmake +++ b/cmake/options.cmake @@ -9,5 +9,4 @@ option(WARNINGS_AS_ERRORS "Compiler warnings as errors" "OFF") option(OPT_ASAN "Use adress sanitizer (debug)" "ON") option(BUILD_TESTING "Build tests." "ON") option(BUILD_BENCHMARKS "Build benchmarks." "OFF") -option(BUILD_DIAGNOSTICS "Build numerical diagnostics." "OFF") option(CODE_COVERAGE "Code coverage." "OFF") diff --git a/cmake/printInfo.cmake b/cmake/printInfo.cmake index 0b2c2ac..254fa14 100755 --- a/cmake/printInfo.cmake +++ b/cmake/printInfo.cmake @@ -14,6 +14,5 @@ message( STATUS "CMAKE_CXX_FLAGS_RELEASE= ${CMAKE_CXX_FLAGS_RELEASE}") message( STATUS ) message( STATUS "BUILD_TESTING= ${BUILD_TESTING}") message( STATUS "BUILD_BENCHMARKS= ${BUILD_BENCHMARKS}") -message( STATUS "BUILD_DIAGNOSTICS= ${BUILD_DIAGNOSTICS}") message( STATUS "CODE_COVERAGE= ${CODE_COVERAGE}") message( STATUS ) diff --git a/diagnostic/CMakeLists.txt b/diagnostic/CMakeLists.txt deleted file mode 100644 index b27293b..0000000 --- a/diagnostic/CMakeLists.txt +++ /dev/null @@ -1,6 +0,0 @@ -add_executable(kde1d-boundary-diagnostic boundary_diagnostic.cpp) -target_link_libraries(kde1d-boundary-diagnostic kde1d) -set_target_properties( - kde1d-boundary-diagnostic - PROPERTIES RUNTIME_OUTPUT_DIRECTORY ${PROJECT_BINARY_DIR}/bin -) diff --git a/diagnostic/NATIVE_RESULTS.md b/diagnostic/NATIVE_RESULTS.md index f39455f..dcdfd56 100644 --- a/diagnostic/NATIVE_RESULTS.md +++ b/diagnostic/NATIVE_RESULTS.md @@ -1,135 +1,52 @@ -# Native boundary-expert validation +# Native boundary-expert evidence -## Statistical validation +The final comparison with the pre-PR estimator has not yet been run. Its +protocol is in [`README.md`](README.md). In particular, the one-sided primary +benchmark will be the actual production log-transform fit from pre-PR `main`, +not the unrepaired fourth-root fit used during development. -The native candidate was compared with commit `4f3d148`, immediately before -the expert implementation. The paired experiment used 100 replications at -$n=25,100,1000,2000$. One-sided scenarios were Exponential, half-normal, -Gamma$(2)$, Gamma$(0.75)$, and Lomax$(2)$; two-sided scenarios were Uniform and -six symmetric or asymmetric beta densities. Ratios below average the -scenario-specific ratios of mean ISE. Parentheses contain paired Monte Carlo -standard errors. +The following implementation checks remain relevant to the selected method. -| support | $n$ | global ISE ratio | boundary ISE ratio | -|---|---:|---:|---:| -| one-sided | 25 | 0.932 (0.008) | 0.896 (0.016) | -| one-sided | 100 | 0.929 (0.009) | 0.903 (0.016) | -| one-sided | 1000 | 0.907 (0.012) | 0.857 (0.017) | -| one-sided | 2000 | 0.881 (0.015) | 0.824 (0.020) | -| two-sided | 25 | 0.874 (0.021) | 0.862 (0.020) | -| two-sided | 100 | 0.911 (0.008) | 0.917 (0.007) | -| two-sided | 1000 | 0.939 (0.007) | 0.954 (0.006) | -| two-sided | 2000 | 0.944 (0.007) | 0.955 (0.006) | +## Selected implementation -Average integrated variance ratios range from 0.93 to 0.94 one-sided and from -0.87 to 0.96 two-sided. Boundary variance ratios range from 0.88 to 0.90 and -from 0.86 to 0.97, respectively. The extra small-sample bias is the intended -price for smoother boundary realizations; at $n=1000,2000$, average integrated -squared bias is also lower than baseline. +- Finite endpoints use the equal average of local-linear and local-quadratic + Gaussian equivalent kernels; the same expert is used for bulk degrees zero, + one, and two. +- Both kernels share an automatically selected degree-two bandwidth. Selection + uses all positive-weight observations on bounded support and the closest 75% + by row count on one-sided support. A manual bandwidth controls only the bulk; + the public multiplier scales both bandwidths. +- Public case weights are used by the classifier, expert estimand, expert + bandwidth selector, effective sample size, and influence approximation. +- A cubic CDF-based fusion region has probability width + $\min(0.25,n_e^{-1/2})$. Endpoints classified as exploding, vanishing, or + ambiguous retain the bulk fit. -The main accepted losses remain the difficult shapes identified by the R -experiments. At $n=2000$, Gamma$(0.75)$ has global/boundary ratios -1.085/1.098, Beta$(0.75,2)$ has 1.075/1.072, and the reflected -Beta$(2,0.75)$ has 1.027/1.026. Gamma$(2)$ and Beta$(2,2)$ select bulk in every -large-sample replication and are exactly unchanged. Uniform, Beta$(1,2)$, and -Beta$(2,1)$ have $n=2000$ global ratios 0.844, 0.817, and 0.830. +## FFT accuracy and runtime -The deterministic native tests cover lower/upper reflection, independent -two-sided endpoint decisions, exploding/vanishing fallback, and affine support -changes. Their golden values were refreshed for the simplified evaluator. +The endpoint kernels are pointwise combinations of an ordinary Gaussian KDE +and its first two derivatives, evaluated on a shared 256-bin FFT grid. In the +100-replication development suite, the mean relative ISE perturbation from FFT +binning was at most 0.011% in every support/sample-size group. Among active +experts, the median absolute paired ISE change was 0.023%, the 99th percentile +was 0.18%, and the maximum was 0.66%. -## Runtime simplification ablation +The direct-kernel fallback was rejected. Across 51--401 output grid points at +$n=25,100$, always using FFT slowed the worst case by 1.25x. On the default +grid at $n=100$, one active endpoint changed from 0.64 to 0.67 ms and two +active endpoints from 0.77 to 0.74 ms. At $n=2000$, FFT reduced one-endpoint +fit time from 1.21 to 0.92 ms and two-endpoint time from 2.25 to 0.96 ms. -The direct native evaluator was simplified after the main validation. The -local-linear and local-quadratic equivalent kernels now share the degree-2 -bandwidth and are averaged in one observation loop. On bounded support this -bandwidth uses all endpoint distances; on one-sided support it uses the closest -75%. Endpoint kernels are evaluated only where their smooth fusion weights are -nonzero, Gaussian terms beyond six bandwidths are omitted, and the fused grid -is normalized once at the end. +## EDF approximation -A paired 100-replication check compared this implementation with commit -`cbde530` over Exponential, half-normal, Gamma$(2)$, Gamma$(0.75)$, Lomax$(2)$, -Uniform, Beta$(1,2)$, Beta$(0.75,2)$, Beta$(0.75,0.75)$, and Beta$(2,2)$. -Ratios compare the simplified evaluator with `cbde530`; parentheses contain -paired Monte Carlo standard errors: - -| support | $n$ | global ISE ratio | boundary ISE ratio | -|---|---:|---:|---:| -| one-sided | 25 | 0.996 (0.002) | 0.999 (0.004) | -| one-sided | 100 | 0.983 (0.003) | 0.982 (0.003) | -| one-sided | 1000 | 0.993 (0.003) | 0.992 (0.003) | -| one-sided | 2000 | 0.992 (0.003) | 0.991 (0.003) | -| two-sided | 25 | 1.010 (0.003) | 1.014 (0.006) | -| two-sided | 100 | 0.999 (0.002) | 1.002 (0.004) | -| two-sided | 1000 | 0.999 (0.003) | 0.992 (0.004) | -| two-sided | 2000 | 0.994 (0.003) | 0.986 (0.004) | - -The largest scenario-level increases were about 3.5% for Gamma$(0.75)$ and -3.9% for Beta$(0.75,0.75)$; Uniform, Beta$(1,2)$, Exponential, half-normal, -and Lomax generally improved. This supports the simpler shared-bandwidth -kernel average without a material aggregate accuracy cost. - -## EDF check - -The conditional mixture EDF was compared with +The conditional mixture EDF was checked against $$ 1+\sum_i\{\log\widehat f(X_i)-\log\widehat f_{-i}(X_i)\}. $$ -For deterministic finite-endpoint samples at $n=25,50,100$, the discrepancy -was 0.08--0.30 EDF units for Uniform and Exponential examples. The asymmetric -Beta$(1,2)$ discrepancy was 0.27--0.33 at $n=50,100$ and 0.84 at $n=25$. -This is adequate for the existing asymptotic EDF convention and does not -justify a weight-derivative correction. Pure-bulk fits retain the old EDF -exactly. - -## Fit time - -Release builds were timed against `4f3d148`. Bulk-classified fits incur only -sorting and remain close to baseline. With a 401-point output grid, the -simplified active-expert timings are: - -| active endpoints | $n=100$ | $n=1000$ | $n=2000$ | -|---|---:|---:|---:| -| one | 0.65 ms (1.7x) | 0.94 ms (2.0x) | 1.22 ms (2.1x) | -| two | 0.78 ms (2.0x) | 1.63 ms (3.7x) | 2.26 ms (4.4x) | - -Relative to `cbde530`, this is a speedup of 2.6--8.7x for one active endpoint -and 3.7--8.3x for two. Absolute expert-fit cost remains below 2.3 ms at -$n=2000$ in this benchmark. - -### FFT evaluation - -The endpoint kernel can be written as a pointwise combination of an ordinary -Gaussian KDE and its first two derivatives. The implementation now evaluates -these three translation-invariant convolutions on a regular 256-bin grid and -interpolates them to the endpoint grid. - -Against the direct endpoint evaluator, total fit times with the default -401-point grid were: - -| active endpoints | $n$ | direct | FFT | speedup | -|---|---:|---:|---:|---:| -| one | 1000 | 0.93 ms | 0.78 ms | 1.19x | -| one | 2000 | 1.21 ms | 0.92 ms | 1.32x | -| two | 1000 | 1.62 ms | 0.84 ms | 1.93x | -| two | 2000 | 2.25 ms | 0.96 ms | 2.35x | - -The direct-kernel fallback was removed after a separate $n=25,100$ benchmark. -Across 51--401 grid points, the worst total-fit slowdown from always using FFT -was 1.25x. With the default grid at $n=100$, one endpoint slowed from 0.64 to -0.67 ms while two endpoints improved slightly from 0.77 to 0.74 ms. In the -100-replication validation suite, the mean relative ISE perturbation from FFT -binning was at most 0.011% for every support/sample-size group. Among fits -whose endpoint expert was active, the median absolute paired ISE change was -0.023%, the 99th percentile was 0.18%, and the maximum was 0.66%. - -## Reproduction - -Install the package with a clean native rebuild at each revision and run -`validate_native_boundary_experts.R`, giving each run a distinct method label -and output file. The script writes replication-level ISE/EDF/log-likelihood and -a companion bias/variance summary. Join the two raw files by support, -scenario, sample size, and replication for paired ratios and uncertainty. +For deterministic finite-endpoint samples at $n=25,50,100$, discrepancies +were 0.08--0.30 EDF units for Uniform and Exponential examples. For +Beta$(1,2)$ they were 0.27--0.33 at $n=50,100$ and 0.84 at $n=25$. This was +considered adequate for an asymptotic trace approximation that already holds +bandwidths fixed. Pure-bulk fits retain the prior EDF calculation exactly. diff --git a/diagnostic/README.md b/diagnostic/README.md index 85687d3..b3d7eec 100644 --- a/diagnostic/README.md +++ b/diagnostic/README.md @@ -1,42 +1,48 @@ -# Boundary diagnostics +# Boundary-expert validation -The diagnostic sweep evaluates deterministic samples from distributions with -known densities and CDFs. It covers finite and one-sided supports, support -scales from `1e-4` to `1e4`, polynomial degrees 0--2, grid sizes 100--1,000, -and fixed or automatically selected bandwidths. Evaluation points approach the -boundary on a logarithmic scale. +This directory contains the retained validation path for the native estimator. +The estimator itself, including the support transforms, endpoint classifier, +boundary kernels, fusion, bandwidth handling, and EDF approximation, is +documented in [`../docs/overview-continuous.dox`](../docs/overview-continuous.dox). -Generate the raw CSV data and an optional summary and PDF with: +## Final comparison -```sh -diagnostic/run_boundary_diagnostics.sh > boundary-diagnostics.csv -Rscript diagnostic/plot_boundary_diagnostics.R boundary-diagnostics.csv -``` +`validate_native_boundary_experts.R` evaluates one installed implementation at +a time. Run it with these method labels: -The executable is deliberately not registered with CTest. Its output is for -comparing numerical behavior between revisions; stable invariants discovered -through the sweep should be promoted to focused regression tests. +| method | installed revision | estimator | +|---|---|---| +| `pre-pr` | pre-PR `main` (`1260b5e` for the planned comparison) | production log transform on one-sided support and probit transform on two-sided support | +| `bulk` | candidate | fourth-root/probit bulk with `boundary_repair = FALSE` | +| `expert` | candidate | fourth-root/probit bulk with the selected boundary experts | -The summary reports four complementary diagnostics: +Using the actual pre-PR revision is intentional: emulating its log transform in +the candidate would miss other grid and numerical behavior of the production +benchmark. -- PDF and CDF error against known distributions near the boundary; -- equivariance when the same data are expressed at different scales; -- agreement between left-bounded fits and reflected right-bounded fits; -- sensitivity to the interpolation grid size. +The suite covers lower- and upper-bounded versions of five one-sided densities +at scales `1e-4`, `1`, and `1e4`, seven two-sided densities, and sample sizes +25, 100, 1,000, and 2,000. It writes replication-level global and boundary ISE, +EDF, and log-likelihood, plus integrated squared bias and variance summaries. +Paired seeds are shared across methods. -The metrics deliberately remain separate. Relative density error is not useful -where the true density vanishes, while CDF error can remain small despite a -severely unstable pointwise density. Candidate repairs should therefore be -checked against both finite nonzero boundary densities and densities that tend -to zero. +From the R-package root, install each requested revision into a separate +library and run, for example: -The separate transformation-boundary investigation, its retained simulation -results, and its current recommendations live in -[`boundary-repair/`](boundary-repair/README.md). +```sh +Rscript inst/include/kde1d-cpp/diagnostic/validate_native_boundary_experts.R \ + pre-pr diagnostic-results/pre-pr.csv 100 /path/to/pre-pr-library +Rscript inst/include/kde1d-cpp/diagnostic/validate_native_boundary_experts.R \ + bulk diagnostic-results/bulk.csv 100 /path/to/candidate-library +Rscript inst/include/kde1d-cpp/diagnostic/validate_native_boundary_experts.R \ + expert diagnostic-results/expert.csv 100 /path/to/candidate-library +``` -The follow-up for supports with exactly one finite endpoint lives in -[`one-sided-repair/`](one-sided-repair/README.md). +Generated CSVs and figures are not versioned. The final aggregate comparison +and representative plots should be recorded in `NATIVE_RESULTS.md` after the +validation is complete. -The shared native implementation is evaluated by -[`validate_native_boundary_experts.R`](validate_native_boundary_experts.R), -with current results summarized in [`NATIVE_RESULTS.md`](NATIVE_RESULTS.md). +`NATIVE_RESULTS.md` currently retains only implementation-level evidence that +still applies to the selected estimator. Superseded R prototypes, candidate +estimators, tuning outputs, and the standalone C++ diagnostic were removed; +stable numerical properties are covered by the unit and invariant tests. diff --git a/diagnostic/boundary-repair/HANDOFF.md b/diagnostic/boundary-repair/HANDOFF.md deleted file mode 100644 index 3d66ef0..0000000 --- a/diagnostic/boundary-repair/HANDOFF.md +++ /dev/null @@ -1,51 +0,0 @@ -# Two-boundary repair handoff - -## Current state - -The directory now contains one experimental estimator for continuous data -with two known finite bounds. It fits the current probit bulk estimator once, -adds an averaged local-linear/local-quadratic kernel expert for confidently -finite endpoints, and otherwise reuses bulk. The kernels share one degree-2 -bandwidth and smooth CDF-scale weights shrink as $n^{-1/2}$. The -finite-endpoint classifier uses -$k=\min(n-1,\lceil2\sqrt n\rceil)$ order statistics and a 95% decision. - -There is no exploding-tail expert, power warp, transformation offset, or CV -selector. Superseded oversmoothing and offset code and outputs were removed. -The retained 100-replication validation and classifier ablation are summarized -in `RESULTS.md`. - -## Reproduce - -From the R-package root: - -```sh -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R 100 -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R -``` - -For a smoke test, pass a smaller replication count and temporary output path -as the first two arguments to either simulation script. - -## Known limitations - -- The R reference assumes support $[0,1]$; native code must apply an affine - map for arbitrary finite bounds. -- Weighted observations have not been specified or validated for the tail - index or shrinking weights. -- The finite-versus-bulk decision is hard, so between-sample endpoint behavior - can still change discretely. -- Before release, test affine support changes, weaker and stronger endpoint - singularities, interior modes, ties, and weighted data. - -## Next work - -The immediate next investigation is the analogous one-sided estimator. Keep -that work in a separate sibling diagnostic directory so this two-boundary -reference remains stable. Native implementation of this estimator should -follow `NATIVE_CPP.md` after the one-sided design has settled enough to assess -shared infrastructure. - -Unrelated top-level generated documentation changes were left untouched. diff --git a/diagnostic/boundary-repair/NATIVE_CPP.md b/diagnostic/boundary-repair/NATIVE_CPP.md deleted file mode 100644 index 45608d8..0000000 --- a/diagnostic/boundary-repair/NATIVE_CPP.md +++ /dev/null @@ -1,5 +0,0 @@ -# Native C++ implementation plan - -The canonical native roadmap now covers the shared one- and two-sided -boundary-expert implementation. See -[`../one-sided-repair/NATIVE_CPP.md`](../one-sided-repair/NATIVE_CPP.md). diff --git a/diagnostic/boundary-repair/README.md b/diagnostic/boundary-repair/README.md deleted file mode 100644 index 0fbb4e6..0000000 --- a/diagnostic/boundary-repair/README.md +++ /dev/null @@ -1,68 +0,0 @@ -# Two-sided boundary repair - -This directory contains the selected experimental estimator for continuous -densities on a known finite interval, its paired validation against the -current probit estimator, and the retained endpoint-classifier ablation. - -## Selected estimator - -The reference implementation assumes the support has been mapped affinely to -$[0,1]$. First fit the current unweighted probit estimator $\widehat f_B$ and -use its CDF to define sample-shrinking endpoint weights. With -$r_n=\min(0.25,n^{-1/2})$ and $s(t)=3t^2-2t^3$, - -$$ -w_L(x)=1-s\left(\min\left\{1,\frac{\widehat F_B(x)}{r_n}\right\}\right), -\qquad -w_U(x)=1-s\left(\min\left\{1,\frac{1-\widehat F_B(x)}{r_n}\right\}\right), -$$ - -and $w_B(x)=1-w_L(x)-w_U(x)$. The finite-boundary expert averages Gaussian -equivalent-kernel local-linear and local-quadratic kernels using one degree-2 -bandwidth selected from all endpoint distances. Density contributions remain -unweighted, so the estimand does not change. The native evaluator computes the -expert only where its fusion weight is nonzero, truncates negative values, and -normalizes once after fusion. - -Finite endpoint behavior is identified from -$k=\min(n-1,\lceil2\sqrt n\rceil)$ order statistics. At the lower endpoint, - -$$ -\widehat\beta_L -= -\frac{k}{\sum_{i=1}^k -\log\{X_{(k+1)}/X_{(i)}\}}, -$$ - -with the analogous calculation on $1-X$ at the upper endpoint. The finite -expert is used if -$\widehat\beta\geq0.9$ and -$\widehat\beta(1-1.645/\sqrt{k})\leq1$; otherwise the endpoint reuses the bulk -estimator. Thus exploding, vanishing, and ambiguous endpoints require no -additional fit. - -The finite or bulk endpoint components are fused with $w_L,w_B,w_U$, -truncated at zero, and normalized numerically. There is no power transform, -offset transform, oversmoothed tail expert, or cross-validation selector. - -## Retained files - -- `scripts/bounded_estimator.R`: pre-native tuning implementation. -- `scripts/validate_bounded_estimator.R`: paired validation against current. -- `scripts/plot_bounded_estimator_validation.R`: numerical and realization - report. -- `scripts/ablate_endpoint_classifier.R`: paired classifier ablation. -- `scripts/plot_endpoint_classifier_ablation.R`: classifier report. -- `results/` and `plots/`: corresponding 100-replication outputs. -- `RESULTS.md`: final numerical conclusions. -- `HANDOFF.md`: concise continuation state. -- `NATIVE_CPP.md`: pointer to the shared one- and two-sided native roadmap. - -Run from the R-package root: - -```sh -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R 100 -Rscript inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R -``` diff --git a/diagnostic/boundary-repair/RESULTS.md b/diagnostic/boundary-repair/RESULTS.md deleted file mode 100644 index 128f69e..0000000 --- a/diagnostic/boundary-repair/RESULTS.md +++ /dev/null @@ -1,59 +0,0 @@ -# Validation results - -## Final estimator - -The final two-boundary estimator combines the current probit bulk fit with an -equal local-linear/local-quadratic expert at endpoints classified as finite. -All other endpoint types reuse bulk. The validation uses 100 paired -replications for Uniform, Beta$(1,2)$, Beta$(0.75,2)$, and -Beta$(0.75,0.75)$ at $n=100,1000,2000$. The primary measure is integrated -squared error (ISE). - -Global ISE ratios to the current bounded estimator are: - -| density | $n=100$ | $n=1000$ | $n=2000$ | -|---|---:|---:|---:| -| Uniform | 0.884 | 0.830 | 0.814 | -| Beta$(1,2)$ | 0.879 | 0.818 | 0.802 | -| Beta$(0.75,2)$ | 0.943 | 1.050 | 1.045 | -| Beta$(0.75,0.75)$ | 0.945 | 1.037 | 1.033 | - -Mean ratios across the four densities are 0.913, 0.934, and 0.923. The -finite-endpoint cases improve clearly. Losses for exploding densities are -small and accepted in exchange for keeping a generic, shape-agnostic finite -expert. - -All retained estimates are nonnegative and normalized numerically. The -maximum mass error in the validation is $2.2\times10^{-16}$. - -## Endpoint classifier - -The selected rule uses one tail-index estimate with -$k=\min(n-1,\lceil2\sqrt n\rceil)$ and a 95% finite-endpoint decision. It was -compared with single scales $\sqrt n$ and $1.5\sqrt n$, and multiscale median -and voting rules. Mean ISE ratios to current are: - -| $n$ | $\sqrt n$, 95% | $2\sqrt n$, 95% | multiscale vote, 90% | -|---:|---:|---:|---:| -| 100 | 0.885 | 0.912 | 0.919 | -| 1000 | 0.976 | 0.936 | 0.996 | -| 2000 | 0.994 | 0.921 | 0.981 | - -The smaller scale is slightly better at $n=100$, but $2\sqrt n$ is clearly -better at $n=1000,2000$ and substantially reduces the worst exploding-tail -loss. Multiscale classification adds complexity without improving ISE or the -representative fits. - -## Bulk decision for nonfinite endpoints - -A final focused comparison used asymmetric Beta$(a,2)$ and symmetric -Beta$(a,a)$ densities for $a=0.9,0.75,0.6$. An oversmoothed probit tail reduced -integrated variance by roughly one third, but its mean ISE ratios to simply -reusing bulk were 0.948, 1.079, and 1.095 at $n=100,1000,2000$. Bulk won all -six large-sample scenarios. The additional transformed fit, offset, bandwidth -multiplier, and fusion branch were therefore removed from the selected -estimator. - -The retained CSVs contain global and endpoint-local ISE, squared bias, -integrated variance, selection rates, minimum density, and mass error. 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-"beta-0.75-0.75",2000,100,"single-1.5-95",0.00713066662475509,0.0027464281638779,0.00438423846087719,0.00318155231896237,0.00133992409120143,0.00184162822776094,0.00347775798206784,0.00139074625748771,0.00208701172458013,0.94,0.93,0.06,0.07,0.793775176927469,1.11022302462516e-16 -"beta-0.75-0.75",2000,100,"single-2-95",0.00706075203244803,0.00273322696679824,0.00432752506564979,0.003194836709572,0.00134366972475958,0.00185116698481242,0.00339375219571971,0.00137397305064016,0.00201977914507954,0.94,0.96,0.06,0.04,0.37705599508214,1.11022302462516e-16 -"beta-0.75-0.75",2000,100,"median-90",0.0075581872325074,0.0028437896946846,0.0047143975378228,0.0034810219983618,0.00140846040120306,0.00207256159715873,0.00360446463231341,0.00141899086237187,0.00218547376994154,0.88,0.9,0.12,0.1,0.793775176927469,1.11022302462516e-16 -"beta-0.75-0.75",2000,100,"vote-90",0.00756867245068476,0.00285026956433839,0.00471840288634637,0.00348103301206084,0.00140849467309012,0.00207253833897071,0.00361509248622447,0.00142545271887366,0.00218963976735082,0.88,0.91,0.12,0.09,0.37705599508214,1.11022302462516e-16 -"beta-0.75-0.75",2000,100,"vote-95",0.00871945752096456,0.00320121654235764,0.00551824097860691,0.00416036224794122,0.00162157367055352,0.0025387885773877,0.00408287571203191,0.0015617130318416,0.00252116268019031,0.77,0.82,0.23,0.18,0.793775176927469,1.11022302462516e-16 diff --git a/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R b/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R deleted file mode 100644 index 65cf569..0000000 --- a/diagnostic/boundary-repair/scripts/ablate_endpoint_classifier.R +++ /dev/null @@ -1,235 +0,0 @@ -# Paired ablation of order-statistic endpoint classifiers. -# Run from the root of the kde1d R package. - -if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { - stop("run from the kde1d package root with pkgload installed") -} -pkgload::load_all(".", quiet = TRUE) -source(paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", - "bounded_estimator.R" -)) - -arguments <- commandArgs(trailingOnly = TRUE) -replication_count <- if (length(arguments) >= 1L) { - as.integer(arguments[[1L]]) -} else { - 100L -} -output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", - "endpoint-classifier-ablation.csv" -) -if (length(arguments) > 2L || !is.finite(replication_count) || - replication_count < 2L) { - stop("usage: ablate_endpoint_classifier.R [replications] [output.csv]") -} - -make_beta_distribution <- function(shape1, shape2, endpoint_truth) { - list( - random = function(sample_size) rbeta(sample_size, shape1, shape2), - density = function(values) dbeta(values, shape1, shape2), - endpoint_truth = endpoint_truth - ) -} -validation_distributions <- list( - uniform = list( - random = runif, - density = dunif, - endpoint_truth = c(lower = "finite", upper = "finite") - ), - `beta-1-2` = make_beta_distribution( - 1, 2, c(lower = "finite", upper = "bulk") - ), - `beta-0.75-2` = make_beta_distribution( - 0.75, 2, c(lower = "bulk", upper = "bulk") - ), - `beta-0.75-0.75` = make_beta_distribution( - 0.75, 0.75, c(lower = "bulk", upper = "bulk") - ) -) -sample_sizes <- c(100L, 1000L, 2000L) -classifier_methods <- c( - "single-95", "single-1.5-95", "single-2-95", - "median-90", "vote-90", "vote-95" -) -methods <- c("kde-current", classifier_methods) -evaluation_points <- sort(unique(c( - 10^seq(-10, -2, length.out = 101L), - seq(0.01, 0.99, length.out = 301L), - 1 - 10^seq(-2, -10, length.out = 101L) -))) -left_points <- evaluation_points <= 0.1 -right_points <- evaluation_points >= 0.9 -result_rows <- list() - -make_classifier_selections <- function(observations) { - list( - `single-95` = select_bounded_endpoint_experts_single_scale(observations), - `single-1.5-95` = select_bounded_endpoint_experts_single_scale( - observations, - tail_multiplier = 1.5 - ), - `single-2-95` = select_bounded_endpoint_experts_single_scale( - observations, - tail_multiplier = 2 - ), - `median-90` = select_bounded_endpoint_experts_multiscale( - observations, - evidence_threshold = qnorm(0.90), - rule = "median" - ), - `vote-90` = select_bounded_endpoint_experts_multiscale( - observations, - evidence_threshold = qnorm(0.90), - rule = "vote" - ), - `vote-95` = select_bounded_endpoint_experts_multiscale( - observations, - evidence_threshold = qnorm(0.95), - rule = "vote" - ) - ) -} - -summarize_estimates <- function(estimates, true_density, region_points) { - mean_density <- rowMeans(estimates) - integrated_errors <- vapply( - seq_len(ncol(estimates)), - function(replication) { - trapezoid_integral( - evaluation_points[region_points], - (estimates[region_points, replication] - - true_density[region_points])^2 - ) - }, - numeric(1L) - ) - c( - ise = mean(integrated_errors), - squared_bias = trapezoid_integral( - evaluation_points[region_points], - (mean_density[region_points] - true_density[region_points])^2 - ), - variance = trapezoid_integral( - evaluation_points[region_points], - rowMeans((estimates[region_points, , drop = FALSE] - - mean_density[region_points])^2) - ) - ) -} - -for (distribution_index in seq_along(validation_distributions)) { - true_density <- validation_distributions[[distribution_index]]$density( - evaluation_points - ) - for (sample_size in sample_sizes) { - estimates <- setNames( - lapply(methods, function(method) { - matrix(NA_real_, length(evaluation_points), replication_count) - }), - methods - ) - choices <- setNames( - lapply(classifier_methods, function(method) { - matrix( - NA_character_, replication_count, 2L, - dimnames = list(NULL, c("lower", "upper")) - ) - }), - classifier_methods - ) - for (replication in seq_len(replication_count)) { - set.seed( - 20260909L + 100000L * distribution_index + - 1000L * match(sample_size, sample_sizes) + replication - ) - observations <- validation_distributions[[distribution_index]]$random( - sample_size - ) - estimates$`kde-current`[, replication] <- normalize_density( - evaluation_points, - dkde1d( - evaluation_points, - kde1d(observations, xmin = 0, xmax = 1) - ) - ) - estimator_components <- fit_bounded_estimator_components( - observations, - evaluation_points - ) - classifier_selections <- make_classifier_selections(observations) - for (method in classifier_methods) { - estimator_components$selection <- classifier_selections[[method]] - estimates[[method]][, replication] <- - fuse_bounded_estimator_components( - evaluation_points, - estimator_components - )$density - choices[[method]][replication, ] <- - classifier_selections[[method]]$expert_choices - } - } - for (method in methods) { - global_summary <- summarize_estimates( - estimates[[method]], true_density, rep(TRUE, length(evaluation_points)) - ) - left_summary <- summarize_estimates( - estimates[[method]], true_density, left_points - ) - right_summary <- summarize_estimates( - estimates[[method]], true_density, right_points - ) - endpoint_truth <- validation_distributions[[distribution_index]]$endpoint_truth - result_rows[[length(result_rows) + 1L]] <- data.frame( - distribution = names(validation_distributions)[[distribution_index]], - sample_size = sample_size, - replications = replication_count, - method = method, - global_ise = global_summary[["ise"]], - global_squared_bias = global_summary[["squared_bias"]], - global_variance = global_summary[["variance"]], - left_ise = left_summary[["ise"]], - left_squared_bias = left_summary[["squared_bias"]], - left_variance = left_summary[["variance"]], - right_ise = right_summary[["ise"]], - right_squared_bias = right_summary[["squared_bias"]], - right_variance = right_summary[["variance"]], - lower_accuracy = if (method == "kde-current") { - NA_real_ - } else { - mean(choices[[method]][, "lower"] == endpoint_truth[["lower"]]) - }, - upper_accuracy = if (method == "kde-current") { - NA_real_ - } else { - mean(choices[[method]][, "upper"] == endpoint_truth[["upper"]]) - }, - lower_finite_rate = if (method == "kde-current") NA_real_ else - mean(choices[[method]][, "lower"] == "finite"), - upper_finite_rate = if (method == "kde-current") NA_real_ else - mean(choices[[method]][, "upper"] == "finite"), - minimum_density = min(estimates[[method]]), - maximum_mass_error = max(abs(vapply( - seq_len(replication_count), - function(replication) { - trapezoid_integral( - evaluation_points, - estimates[[method]][, replication] - ) - 1 - }, - numeric(1L) - ))) - ) - } - message( - names(validation_distributions)[[distribution_index]], - ", n = ", sample_size - ) - } -} - -results <- do.call(rbind, result_rows) -dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) -write.csv(results, output_file, row.names = FALSE) -message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary-repair/scripts/bounded_estimator.R b/diagnostic/boundary-repair/scripts/bounded_estimator.R deleted file mode 100644 index 7ef12c0..0000000 --- a/diagnostic/boundary-repair/scripts/bounded_estimator.R +++ /dev/null @@ -1,376 +0,0 @@ -# Reference R implementation of the selected two-sided boundary estimator. - -trapezoid_integral <- function(evaluation_points, values) { - sum(diff(evaluation_points) * - (values[-length(values)] + values[-1L]) / 2) -} - -normalize_density <- function(evaluation_points, density) { - density <- pmax(0, density) - density_mass <- trapezoid_integral(evaluation_points, density) - if (!is.finite(density_mass) || density_mass <= 0) { - stop("density cannot be normalized") - } - density / density_mass -} - -smoothstep <- function(normalized_distance) { - 3 * normalized_distance^2 - 2 * normalized_distance^3 -} - -make_bounded_expert_weights <- function(probabilities, sample_size, - concentration = 1, - shrinkage_exponent = 0.5) { - boundary_fraction <- min( - 0.25, - concentration / sample_size^shrinkage_exponent - ) - lower_weights <- 1 - smoothstep(pmin(1, probabilities / boundary_fraction)) - upper_weights <- 1 - smoothstep(pmin( - 1, - (1 - probabilities) / boundary_fraction - )) - cbind( - lower = lower_weights, - bulk = pmax(0, 1 - lower_weights - upper_weights), - upper = upper_weights - ) -} - -fit_local_polynomial_boundary <- function( - observations, - evaluation_points, - bandwidth_weights, - minimum_bandwidth, - degree) { - if (!degree %in% c(1, 2)) { - stop("local boundary degree must be 1 or 2") - } - selected_bandwidth <- kde1d( - observations, - weights = bandwidth_weights, - deg = degree - )$bw - bandwidth <- max(selected_bandwidth, minimum_bandwidth) - standardized_boundary <- evaluation_points / bandwidth - truncated_moment_0 <- pnorm(standardized_boundary) - truncated_moment_1 <- -dnorm(standardized_boundary) - truncated_moment_2 <- truncated_moment_0 - - standardized_boundary * dnorm(standardized_boundary) - if (degree == 1) { - moment_determinant <- truncated_moment_0 * truncated_moment_2 - - truncated_moment_1^2 - equivalent_kernel_coefficients <- cbind( - truncated_moment_2 / moment_determinant, - -truncated_moment_1 / moment_determinant - ) - } else { - truncated_moment_3 <- -( - standardized_boundary^2 + 2 - ) * dnorm(standardized_boundary) - truncated_moment_4 <- 3 * truncated_moment_0 - ( - standardized_boundary^3 + 3 * standardized_boundary - ) * dnorm(standardized_boundary) - moment_determinant <- - truncated_moment_0 * ( - truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 - ) - - truncated_moment_1 * ( - truncated_moment_1 * truncated_moment_4 - - truncated_moment_2 * truncated_moment_3 - ) + - truncated_moment_2 * ( - truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 - ) - equivalent_kernel_coefficients <- cbind( - ( - truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 - ) / moment_determinant, - ( - truncated_moment_2 * truncated_moment_3 - - truncated_moment_1 * truncated_moment_4 - ) / moment_determinant, - ( - truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 - ) / moment_determinant - ) - } - density <- numeric(length(evaluation_points)) - for (chunk_start in seq(1L, length(evaluation_points), by = 128L)) { - chunk_indices <- chunk_start:min( - chunk_start + 127L, - length(evaluation_points) - ) - kernel_arguments <- outer( - evaluation_points[chunk_indices], - observations, - "-" - ) / bandwidth - base_kernels <- dnorm(kernel_arguments) - corrected_kernels <- base_kernels * - equivalent_kernel_coefficients[chunk_indices, 1L] - for (polynomial_order in seq_len(degree)) { - corrected_kernels <- corrected_kernels + - base_kernels * - equivalent_kernel_coefficients[ - chunk_indices, - polynomial_order + 1L - ] * kernel_arguments^polynomial_order - } - density[chunk_indices] <- rowMeans(corrected_kernels) / bandwidth - } - list( - density = normalize_density(evaluation_points, density), - bandwidth = bandwidth, - selected_bandwidth = selected_bandwidth - ) -} - -fit_bounded_finite_expert <- function(observations, evaluation_points, - concentration = 1, - shrinkage_exponent = 0.5) { - probability_ranks <- (rank(observations, ties.method = "average") - 0.5) / - length(observations) - bandwidth_weights <- make_bounded_expert_weights( - probability_ranks, - length(observations), - concentration, - shrinkage_exponent - ) - bulk_model <- kde1d(observations, xmin = 0, xmax = 1) - bulk_density <- normalize_density( - evaluation_points, - dkde1d(evaluation_points, bulk_model) - ) - endpoint_densities <- lapply(c(1L, 2L), function(degree) { - minimum_bandwidth <- kde1d(observations, deg = degree)$bw - lower_density <- fit_local_polynomial_boundary( - observations, - evaluation_points, - bandwidth_weights[, "lower"], - minimum_bandwidth, - degree - )$density - upper_density <- rev(fit_local_polynomial_boundary( - 1 - observations, - rev(1 - evaluation_points), - bandwidth_weights[, "upper"], - minimum_bandwidth, - degree - )$density) - cbind(lower = lower_density, bulk = bulk_density, upper = upper_density) - }) - component_densities <- ( - endpoint_densities[[1L]] + endpoint_densities[[2L]] - ) / 2 - evaluation_weights <- make_bounded_expert_weights( - pkde1d(evaluation_points, bulk_model), - length(observations), - concentration, - shrinkage_exponent - ) - list( - density = normalize_density( - evaluation_points, - rowSums(evaluation_weights * component_densities) - ), - component_densities = component_densities, - evaluation_weights = evaluation_weights, - boundary_fraction = min( - 0.25, - concentration / length(observations)^shrinkage_exponent - ) - ) -} - -estimate_bounded_tail_indices <- function(observations, tail_counts) { - if (any(tail_counts < 1L) || any(tail_counts >= length(observations))) { - stop("tail_counts must be between one and sample size minus one") - } - ordered_observations <- sort(observations) - upper_distances <- sort(1 - observations) - tail_indices <- vapply(tail_counts, function(tail_count) { - c( - lower = tail_count / sum(log( - ordered_observations[[tail_count + 1L]] / - pmax( - .Machine$double.eps, - ordered_observations[seq_len(tail_count)] - ) - )), - upper = tail_count / sum(log( - upper_distances[[tail_count + 1L]] / - pmax(.Machine$double.eps, upper_distances[seq_len(tail_count)]) - )) - ) - }, numeric(2L)) - if (length(tail_counts) == 1L) { - tail_indices <- matrix( - tail_indices, - nrow = 2L, - dimnames = list(c("lower", "upper"), NULL) - ) - } - rownames(tail_indices) <- c("lower", "upper") - colnames(tail_indices) <- as.character(tail_counts) - tail_indices -} - -select_bounded_endpoint_experts_single_scale <- function( - observations, - tail_multiplier = 1, - evidence_threshold = qnorm(0.95), - minimum_finite_index = 0.9) { - if (!is.finite(tail_multiplier) || tail_multiplier <= 0) { - stop("tail_multiplier must be finite and positive") - } - tail_count <- min( - length(observations) - 1L, - ceiling(tail_multiplier * sqrt(length(observations))) - ) - tail_indices <- estimate_bounded_tail_indices( - observations, - tail_count - )[, 1L] - expert_choices <- rep("bulk", length(tail_indices)) - names(expert_choices) <- names(tail_indices) - expert_choices[ - tail_indices >= minimum_finite_index & - tail_indices * (1 - evidence_threshold / sqrt(tail_count)) <= 1 - ] <- "finite" - list( - expert_choices = expert_choices, - tail_indices = tail_indices, - tail_count = tail_count, - evidence_threshold = evidence_threshold, - minimum_finite_index = minimum_finite_index - ) -} - -select_bounded_endpoint_experts_multiscale <- function( - observations, - evidence_threshold = qnorm(0.90), - tail_multipliers = c(1, 1.5, 2), - maximum_tail_fraction = 0.15, - rule = c("vote", "median")) { - rule <- match.arg(rule) - tail_counts <- pmin( - floor(maximum_tail_fraction * length(observations)), - ceiling(tail_multipliers * sqrt(length(observations))) - ) - tail_counts <- pmax(1L, pmin(length(observations) - 1L, tail_counts)) - tail_indices <- estimate_bounded_tail_indices(observations, tail_counts) - standardized_indices <- sweep( - log(tail_indices), - 2L, - sqrt(tail_counts), - "*" - ) - expert_choices <- apply(standardized_indices, 1L, function(scores) { - if (rule == "median") { - median_score <- median(scores) - if (abs(median_score) <= evidence_threshold) { - "finite" - } else { - "bulk" - } - } else { - required_votes <- floor(length(scores) / 2) + 1L - if (sum(abs(scores) <= evidence_threshold) >= required_votes) { - "finite" - } else { - "bulk" - } - } - }) - list( - expert_choices = expert_choices, - tail_indices = tail_indices, - standardized_indices = standardized_indices, - tail_counts = tail_counts, - evidence_threshold = evidence_threshold, - tail_multipliers = tail_multipliers, - maximum_tail_fraction = maximum_tail_fraction, - rule = rule - ) -} - -select_bounded_endpoint_experts <- function( - observations, - evidence_threshold = qnorm(0.95), - minimum_finite_index = 0.9) { - select_bounded_endpoint_experts_single_scale( - observations, - tail_multiplier = 2, - evidence_threshold, - minimum_finite_index - ) -} - -fit_bounded_estimator_components <- function( - observations, - evaluation_points, - concentration = 1, - shrinkage_exponent = 0.5) { - if (length(observations) < 4L || any(!is.finite(observations)) || - any(observations < 0 | observations > 1)) { - stop("observations must contain at least four finite values in [0, 1]") - } - if (any(!is.finite(evaluation_points)) || - is.unsorted(evaluation_points, strictly = TRUE) || - any(evaluation_points < 0 | evaluation_points > 1)) { - stop("evaluation_points must be strictly increasing in [0, 1]") - } - finite_fit <- fit_bounded_finite_expert( - observations, - evaluation_points, - concentration, - shrinkage_exponent - ) - selection <- select_bounded_endpoint_experts(observations) - list( - finite_fit = finite_fit, - selection = selection - ) -} - -fuse_bounded_estimator_components <- function( - evaluation_points, - estimator_components) { - finite_fit <- estimator_components$finite_fit - selection <- estimator_components$selection - component_densities <- finite_fit$component_densities - for (boundary in c("lower", "upper")) { - if (selection$expert_choices[[boundary]] != "finite") { - component_densities[, boundary] <- component_densities[, "bulk"] - } - } - list( - density = normalize_density( - evaluation_points, - rowSums(finite_fit$evaluation_weights * component_densities) - ), - component_densities = component_densities, - evaluation_weights = finite_fit$evaluation_weights, - expert_choices = selection$expert_choices, - tail_indices = selection$tail_indices, - tail_count = selection$tail_count, - boundary_fraction = finite_fit$boundary_fraction - ) -} - -fit_bounded_selected_estimator <- function( - observations, - evaluation_points, - concentration = 1, - shrinkage_exponent = 0.5) { - fuse_bounded_estimator_components( - evaluation_points, - fit_bounded_estimator_components( - observations, - evaluation_points, - concentration, - shrinkage_exponent - ) - ) -} diff --git a/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R b/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R deleted file mode 100644 index ddb2597..0000000 --- a/diagnostic/boundary-repair/scripts/plot_bounded_estimator_validation.R +++ /dev/null @@ -1,208 +0,0 @@ -# Plot the paired validation of the selected bounded estimator. -# Run from the root of the kde1d R package. - -if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { - stop("run from the kde1d package root with pkgload installed") -} -pkgload::load_all(".", quiet = TRUE) -source(paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", - "bounded_estimator.R" -)) - -arguments <- commandArgs(trailingOnly = TRUE) -input_file <- if (length(arguments) >= 1L) arguments[[1L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", - "bounded-estimator-validation.csv" -) -output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/plots/", - "bounded-estimator-validation.pdf" -) -if (length(arguments) > 2L) { - stop("usage: plot_bounded_estimator_validation.R [input.csv] [output.pdf]") -} - -results <- read.csv(input_file) -replication_count <- unique(results$replications) -if (length(replication_count) != 1L) { - stop("input must contain a single replication count") -} -method_colors <- c(current = "grey45", selected = "#009E73") -validation_distributions <- list( - uniform = list(random = runif, density = dunif), - `beta-1-2` = list( - random = function(sample_size) rbeta(sample_size, 1, 2), - density = function(values) dbeta(values, 1, 2) - ), - `beta-0.75-2` = list( - random = function(sample_size) rbeta(sample_size, 0.75, 2), - density = function(values) dbeta(values, 0.75, 2) - ), - `beta-0.75-0.75` = list( - random = function(sample_size) rbeta(sample_size, 0.75, 0.75), - density = function(values) dbeta(values, 0.75, 0.75) - ) -) -evaluation_points <- sort(unique(c( - 10^seq(-10, -2, length.out = 101L), - seq(0.01, 0.99, length.out = 301L), - 1 - 10^seq(-2, -10, length.out = 101L) -))) - -pdf(output_file, width = 12, height = 8) -par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) -for (sample_size in sort(unique(results$sample_size))) { - for (distribution in names(validation_distributions)) { - scenario_results <- results[ - results$sample_size == sample_size & - results$distribution == distribution, - ] - current_result <- scenario_results[scenario_results$method == "current", ] - selected_result <- scenario_results[scenario_results$method == "selected", ] - ratios <- c( - ISE = selected_result$global_ise / current_result$global_ise, - bias = selected_result$global_squared_bias / - current_result$global_squared_bias, - variance = selected_result$global_variance / - current_result$global_variance - ) - barplot( - ratios, col = c("grey45", "#E69F00", "#56B4E9"), - ylim = range(c(0, 1, ratios)), ylab = "selected / current", - main = sprintf("%s, n = %d", distribution, sample_size) - ) - abline(h = 1, lty = 2) - } -} -mtext( - sprintf("Selected estimator: %d paired replications", replication_count), - outer = TRUE, font = 2, cex = 1.1 -) - -par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) -for (sample_size in sort(unique(results$sample_size))) { - for (distribution in names(validation_distributions)) { - selected_result <- results[ - results$sample_size == sample_size & - results$distribution == distribution & - results$method == "selected", - ] - barplot( - rbind( - bulk = c(selected_result$lower_bulk_rate, selected_result$upper_bulk_rate), - finite = c( - selected_result$lower_finite_rate, - selected_result$upper_finite_rate - ) - ), - names.arg = c("lower", "upper"), col = c("grey60", "#0072B2"), - ylim = c(0, 1), ylab = "selection rate", - main = sprintf("%s, n = %d", distribution, sample_size) - ) - if (sample_size == min(results$sample_size) && - distribution == names(validation_distributions)[[1L]]) { - legend( - "topright", c("bulk", "finite"), - fill = c("grey60", "#0072B2"), bty = "n", cex = 0.75 - ) - } - } -} -mtext("Effective endpoint components", outer = TRUE, font = 2, cex = 1.1) - -sample_size <- 1000L -for (distribution_index in seq_along(validation_distributions)) { - true_density <- validation_distributions[[distribution_index]]$density( - evaluation_points - ) - par(mfrow = c(2, 3), mar = c(4, 4.2, 2.3, 0.6), oma = c(0, 0, 3, 0)) - for (replication in 1:2) { - set.seed( - 20260906L + 100000L * distribution_index + 1000L * 2L + replication - ) - observations <- validation_distributions[[distribution_index]]$random( - sample_size - ) - selected_fit <- fit_bounded_selected_estimator( - observations, - evaluation_points - ) - estimates <- list( - current = normalize_density( - evaluation_points, - dkde1d( - evaluation_points, - kde1d(observations, xmin = 0, xmax = 1) - ) - ), - selected = selected_fit$density - ) - plot( - evaluation_points, true_density, type = "l", lwd = 3, col = "black", - ylim = c(0, quantile(c(true_density, unlist(estimates)), 0.98)), - xlab = "x", ylab = "density", - main = sprintf( - "realization %d: L=%s, U=%s", - replication, - selected_fit$expert_choices[["lower"]], - selected_fit$expert_choices[["upper"]] - ) - ) - for (method in names(estimates)) { - lines( - evaluation_points, estimates[[method]], col = method_colors[[method]], - lwd = if (method == "selected") 2.5 else 1.5, - lty = match(method, names(estimates)) - ) - } - if (replication == 1L) { - legend( - "topright", c("truth", "current", "selected"), - col = c("black", method_colors), lty = c(1, 1, 2), - lwd = c(3, 1.5, 2.5), bty = "n", cex = 0.75 - ) - } - for (boundary in c("left", "right")) { - boundary_points <- if (boundary == "left") { - evaluation_points >= 1e-6 & evaluation_points <= 0.1 - } else { - evaluation_points >= 0.9 & evaluation_points <= 1 - 1e-6 - } - boundary_distances <- if (boundary == "left") { - evaluation_points[boundary_points] - } else { - 1 - evaluation_points[boundary_points] - } - boundary_order <- order(boundary_distances) - plot( - boundary_distances[boundary_order], - true_density[boundary_points][boundary_order], - type = "l", log = "x", lwd = 3, col = "black", - ylim = c(0, quantile(c( - true_density[boundary_points], - unlist(lapply(estimates, function(density) density[boundary_points])) - ), 0.99)), - xlab = "distance from boundary", ylab = "density", main = boundary - ) - for (method in names(estimates)) { - lines( - boundary_distances[boundary_order], - estimates[[method]][boundary_points][boundary_order], - col = method_colors[[method]], - lwd = if (method == "selected") 2.5 else 1.5, - lty = match(method, names(estimates)) - ) - } - } - } - mtext( - sprintf( - "%s, n = %d; effective choices shown in panel titles", - names(validation_distributions)[[distribution_index]], sample_size - ), - outer = TRUE, font = 2, cex = 1.1 - ) -} -dev.off() -message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R b/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R deleted file mode 100644 index 89b6a40..0000000 --- a/diagnostic/boundary-repair/scripts/plot_endpoint_classifier_ablation.R +++ /dev/null @@ -1,234 +0,0 @@ -# Plot the paired endpoint-classifier ablation and representative fits. -# Run from the root of the kde1d R package. - -if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { - stop("run from the kde1d package root with pkgload installed") -} -pkgload::load_all(".", quiet = TRUE) -source(paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", - "bounded_estimator.R" -)) - -arguments <- commandArgs(trailingOnly = TRUE) -input_file <- if (length(arguments) >= 1L) arguments[[1L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", - "endpoint-classifier-ablation.csv" -) -output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/plots/", - "endpoint-classifier-ablation.pdf" -) -if (length(arguments) > 2L) { - stop("usage: plot_endpoint_classifier_ablation.R [input.csv] [output.pdf]") -} - -results <- read.csv(input_file) -classifier_methods <- c( - "single-95", "single-1.5-95", "single-2-95", - "median-90", "vote-90", "vote-95" -) -method_labels <- c( - `single-95` = "1x", `single-1.5-95` = "1.5x", `single-2-95` = "2x", - `median-90` = "median", `vote-90` = "vote 90", `vote-95` = "vote 95" -) -method_colors <- c( - `single-95` = "#009E73", `single-1.5-95` = "#56B4E9", - `single-2-95` = "#E69F00", `median-90` = "#CC79A7", - `vote-90` = "#7B3294", `vote-95` = "#D55E00" -) -validation_distributions <- list( - uniform = list(random = runif, density = dunif), - `beta-1-2` = list( - random = function(sample_size) rbeta(sample_size, 1, 2), - density = function(values) dbeta(values, 1, 2) - ), - `beta-0.75-2` = list( - random = function(sample_size) rbeta(sample_size, 0.75, 2), - density = function(values) dbeta(values, 0.75, 2) - ), - `beta-0.75-0.75` = list( - random = function(sample_size) rbeta(sample_size, 0.75, 0.75), - density = function(values) dbeta(values, 0.75, 0.75) - ) -) -evaluation_points <- sort(unique(c( - 10^seq(-10, -2, length.out = 101L), - seq(0.01, 0.99, length.out = 301L), - 1 - 10^seq(-2, -10, length.out = 101L) -))) - -dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) -pdf(output_file, width = 12, height = 8) - -par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) -for (sample_size in sort(unique(results$sample_size))) { - for (distribution in names(validation_distributions)) { - scenario_results <- results[ - results$sample_size == sample_size & - results$distribution == distribution, - ] - current_ise <- scenario_results$global_ise[ - scenario_results$method == "kde-current" - ] - scenario_results <- scenario_results[ - match(classifier_methods, scenario_results$method), - ] - ratios <- scenario_results$global_ise / current_ise - barplot( - ratios, - names.arg = method_labels[classifier_methods], - col = method_colors[classifier_methods], las = 2, cex.names = 0.7, - ylim = range(c(0, 1, ratios)), ylab = "global ISE / current", - main = sprintf("%s, n = %d", distribution, sample_size) - ) - abline(h = 1, lty = 2) - } -} -mtext( - sprintf( - "Classifier ISE: %d paired replications", - unique(results$replications) - ), - outer = TRUE, font = 2, cex = 1.1 -) - -par(mfrow = c(3, 4), mar = c(4.5, 4.2, 2.4, 0.5), oma = c(0, 0, 3.5, 0)) -for (sample_size in sort(unique(results$sample_size))) { - for (distribution in names(validation_distributions)) { - scenario_results <- results[ - results$sample_size == sample_size & - results$distribution == distribution & - results$method %in% classifier_methods, - ] - scenario_results <- scenario_results[ - match(classifier_methods, scenario_results$method), - ] - barplot( - rowMeans(scenario_results[, c("lower_accuracy", "upper_accuracy")]), - names.arg = method_labels[classifier_methods], - col = method_colors[classifier_methods], las = 2, cex.names = 0.7, - ylim = c(0, 1), ylab = "mean endpoint accuracy", - main = sprintf("%s, n = %d", distribution, sample_size) - ) - } -} -mtext( - "Classification accuracy (finite versus bulk endpoint component)", - outer = TRUE, font = 2, cex = 1.1 -) - -visual_methods <- c("single-95", "single-2-95", "vote-90") -sample_size <- 1000L -for (distribution_index in seq_along(validation_distributions)) { - true_density <- validation_distributions[[distribution_index]]$density( - evaluation_points - ) - par(mfrow = c(2, 3), mar = c(4, 4.2, 2.4, 0.6), oma = c(0, 0, 3, 0)) - for (replication in 1:2) { - set.seed( - 20260909L + 100000L * distribution_index + 1000L * 2L + replication - ) - observations <- validation_distributions[[distribution_index]]$random( - sample_size - ) - estimator_components <- fit_bounded_estimator_components( - observations, - evaluation_points - ) - selections <- list( - `single-95` = select_bounded_endpoint_experts_single_scale(observations), - `single-2-95` = select_bounded_endpoint_experts_single_scale( - observations, - tail_multiplier = 2 - ), - `vote-90` = select_bounded_endpoint_experts_multiscale( - observations, - evidence_threshold = qnorm(0.90), - rule = "vote" - ) - ) - estimates <- list( - current = normalize_density( - evaluation_points, - dkde1d( - evaluation_points, - kde1d(observations, xmin = 0, xmax = 1) - ) - ) - ) - for (method in visual_methods) { - estimator_components$selection <- selections[[method]] - estimates[[method]] <- fuse_bounded_estimator_components( - evaluation_points, - estimator_components - )$density - } - plot( - evaluation_points, true_density, type = "l", lwd = 3, col = "black", - ylim = c(0, quantile(c(true_density, unlist(estimates)), 0.98)), - xlab = "x", ylab = "density", - main = sprintf("realization %d", replication) - ) - lines(evaluation_points, estimates$current, col = "grey45", lwd = 1.5) - for (method in visual_methods) { - lines( - evaluation_points, estimates[[method]], col = method_colors[[method]], - lwd = if (method == "single-2-95") 2.5 else 1.5, - lty = match(method, visual_methods) - ) - } - if (replication == 1L) { - legend( - "topright", c("truth", "current", method_labels[visual_methods]), - col = c("black", "grey45", method_colors[visual_methods]), - lty = c(1, 1, seq_along(visual_methods)), - lwd = c(3, 1.5, 1.5, 2.5, 1.5), bty = "n", cex = 0.72 - ) - } - for (boundary in c("left", "right")) { - boundary_points <- if (boundary == "left") { - evaluation_points >= 1e-6 & evaluation_points <= 0.1 - } else { - evaluation_points >= 0.9 & evaluation_points <= 1 - 1e-6 - } - boundary_distances <- if (boundary == "left") { - evaluation_points[boundary_points] - } else { - 1 - evaluation_points[boundary_points] - } - boundary_order <- order(boundary_distances) - plot( - boundary_distances[boundary_order], - true_density[boundary_points][boundary_order], - type = "l", log = "x", lwd = 3, col = "black", - ylim = c(0, quantile(c( - true_density[boundary_points], - unlist(lapply(estimates, function(density) density[boundary_points])) - ), 0.98)), - xlab = "distance from boundary", ylab = "density", main = boundary - ) - lines( - boundary_distances[boundary_order], - estimates$current[boundary_points][boundary_order], - col = "grey45", lwd = 1.5 - ) - for (method in visual_methods) { - lines( - boundary_distances[boundary_order], - estimates[[method]][boundary_points][boundary_order], - col = method_colors[[method]], - lwd = if (method == "single-2-95") 2.5 else 1.5, - lty = match(method, visual_methods) - ) - } - } - } - mtext( - sprintf("%s, n = %d", names(validation_distributions)[distribution_index], sample_size), - outer = TRUE, font = 2, cex = 1.1 - ) -} - -dev.off() -message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R b/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R deleted file mode 100644 index 32cddd6..0000000 --- a/diagnostic/boundary-repair/scripts/validate_bounded_estimator.R +++ /dev/null @@ -1,195 +0,0 @@ -# Paired validation of the selected bounded estimator against current kde1d. -# Run from the root of the kde1d R package. - -if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { - stop("run from the kde1d package root with pkgload installed") -} -pkgload::load_all(".", quiet = TRUE) -source(paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/scripts/", - "bounded_estimator.R" -)) - -arguments <- commandArgs(trailingOnly = TRUE) -replication_count <- if (length(arguments) >= 1L) { - as.integer(arguments[[1L]]) -} else { - 100L -} -output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/boundary-repair/results/", - "bounded-estimator-validation.csv" -) -if (length(arguments) > 2L || !is.finite(replication_count) || - replication_count < 2L) { - stop("usage: validate_bounded_estimator.R [replications] [output.csv]") -} - -make_beta_distribution <- function(shape1, shape2) { - list( - random = function(sample_size) rbeta(sample_size, shape1, shape2), - density = function(values) dbeta(values, shape1, shape2) - ) -} -validation_distributions <- list( - uniform = list(random = runif, density = dunif), - `beta-1-2` = make_beta_distribution(1, 2), - `beta-0.75-2` = make_beta_distribution(0.75, 2), - `beta-0.75-0.75` = make_beta_distribution(0.75, 0.75) -) -sample_sizes <- c(100L, 1000L, 2000L) -methods <- c("current", "selected") -evaluation_points <- sort(unique(c( - 10^seq(-10, -2, length.out = 101L), - seq(0.01, 0.99, length.out = 301L), - 1 - 10^seq(-2, -10, length.out = 101L) -))) -left_points <- evaluation_points <= 0.1 -right_points <- evaluation_points >= 0.9 -result_rows <- list() - -summarize_estimates <- function(estimates, true_density, region_points) { - mean_density <- rowMeans(estimates) - integrated_errors <- vapply( - seq_len(ncol(estimates)), - function(replication) { - trapezoid_integral( - evaluation_points[region_points], - (estimates[region_points, replication] - - true_density[region_points])^2 - ) - }, - numeric(1L) - ) - c( - ise = mean(integrated_errors), - ise_median = median(integrated_errors), - squared_bias = trapezoid_integral( - evaluation_points[region_points], - (mean_density[region_points] - true_density[region_points])^2 - ), - variance = trapezoid_integral( - evaluation_points[region_points], - rowMeans((estimates[region_points, , drop = FALSE] - - mean_density[region_points])^2) - ) - ) -} - -for (distribution_index in seq_along(validation_distributions)) { - true_density <- validation_distributions[[distribution_index]]$density( - evaluation_points - ) - for (sample_size in sample_sizes) { - estimates <- setNames( - lapply(methods, function(method) { - matrix(NA_real_, length(evaluation_points), replication_count) - }), - methods - ) - expert_choices <- array( - NA_character_, - dim = c(replication_count, 2L), - dimnames = list(NULL, c("lower", "upper")) - ) - for (replication in seq_len(replication_count)) { - set.seed( - 20260906L + 100000L * distribution_index + - 1000L * match(sample_size, sample_sizes) + replication - ) - observations <- validation_distributions[[distribution_index]]$random( - sample_size - ) - estimates$current[, replication] <- normalize_density( - evaluation_points, - dkde1d( - evaluation_points, - kde1d(observations, xmin = 0, xmax = 1) - ) - ) - estimator_components <- fit_bounded_estimator_components( - observations, - evaluation_points - ) - selected_fit <- fuse_bounded_estimator_components( - evaluation_points, - estimator_components - ) - estimates$selected[, replication] <- selected_fit$density - expert_choices[replication, ] <- selected_fit$expert_choices - } - for (method in methods) { - global_summary <- summarize_estimates( - estimates[[method]], - true_density, - rep(TRUE, length(evaluation_points)) - ) - left_summary <- summarize_estimates( - estimates[[method]], - true_density, - left_points - ) - right_summary <- summarize_estimates( - estimates[[method]], - true_density, - right_points - ) - result_rows[[length(result_rows) + 1L]] <- data.frame( - distribution = names(validation_distributions)[[distribution_index]], - sample_size = sample_size, - replications = replication_count, - method = method, - global_ise = global_summary[["ise"]], - global_ise_median = global_summary[["ise_median"]], - global_squared_bias = global_summary[["squared_bias"]], - global_variance = global_summary[["variance"]], - left_ise = left_summary[["ise"]], - left_squared_bias = left_summary[["squared_bias"]], - left_variance = left_summary[["variance"]], - right_ise = right_summary[["ise"]], - right_squared_bias = right_summary[["squared_bias"]], - right_variance = right_summary[["variance"]], - lower_finite_rate = if (method == "selected") { - mean(expert_choices[, "lower"] == "finite") - } else { - NA_real_ - }, - upper_finite_rate = if (method == "selected") { - mean(expert_choices[, "upper"] == "finite") - } else { - NA_real_ - }, - lower_bulk_rate = if (method == "selected") { - mean(expert_choices[, "lower"] == "bulk") - } else { - NA_real_ - }, - upper_bulk_rate = if (method == "selected") { - mean(expert_choices[, "upper"] == "bulk") - } else { - NA_real_ - }, - minimum_density = min(estimates[[method]]), - maximum_mass_error = max(abs(vapply( - seq_len(replication_count), - function(replication) { - trapezoid_integral( - evaluation_points, - estimates[[method]][, replication] - ) - 1 - }, - numeric(1L) - ))) - ) - } - message( - names(validation_distributions)[[distribution_index]], - ", n = ", sample_size - ) - } -} - -results <- do.call(rbind, result_rows) -dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) -write.csv(results, output_file, row.names = FALSE) -message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/boundary_diagnostic.cpp b/diagnostic/boundary_diagnostic.cpp deleted file mode 100644 index 27cc53a..0000000 --- a/diagnostic/boundary_diagnostic.cpp +++ /dev/null @@ -1,155 +0,0 @@ -#include -#include -#include -#include -#include -#include -#include -#include - -namespace { - -struct Scenario -{ - std::string name; - Eigen::VectorXd observations; - double xmin; - double xmax; - double scale; -}; - -Eigen::VectorXd -probabilities(Eigen::Index size) -{ - return Eigen::VectorXd::LinSpaced( - size, 0.5 / static_cast(size), - 1.0 - 0.5 / static_cast(size)); -} - -Scenario -make_scenario(const std::string& name, Eigen::Index size, double scale) -{ - Eigen::VectorXd probability = probabilities(size); - if (name == "uniform") { - return { name, probability * scale, 0.0, scale, scale }; - } else if (name == "beta-2-1") { - return { name, probability.array().sqrt() * scale, 0.0, scale, scale }; - } else if (name == "beta-1-2") { - return { name, - (1.0 - (1.0 - probability.array()).sqrt()) * scale, - 0.0, - scale, - scale }; - } else if (name == "exponential-left") { - return { name, - (-(1.0 - probability.array()).log()) * scale, - 0.0, - NAN, - scale }; - } - return { name, - (1.0 - probability.array()).log() * scale, - NAN, - 0.0, - scale }; -} - -double -true_pdf(const std::string& name, double position, double scale) -{ - if (name == "uniform") - return 1.0 / scale; - if (name == "beta-2-1") - return 2.0 * position / scale; - if (name == "beta-1-2") - return 2.0 * (1.0 - position) / scale; - return std::exp(-position) / scale; -} - -double -true_cdf(const std::string& name, double position) -{ - if (name == "uniform") - return position; - if (name == "beta-2-1") - return position * position; - if (name == "beta-1-2") - return 1.0 - (1.0 - position) * (1.0 - position); - if (name == "exponential-left") - return 1.0 - std::exp(-position); - return std::exp(-position); -} - -double -evaluation_point(const Scenario& scenario, double position) -{ - if (scenario.name == "exponential-right") - return -position * scenario.scale; - return position * scenario.scale; -} - -void -run_scenario(const Scenario& scenario, - size_t degree, - size_t grid_size, - double bandwidth, - const Eigen::VectorXd& positions) -{ - kde1d::Kde1d fit(scenario.xmin, - scenario.xmax, - "continuous", - 1.0, - bandwidth, - degree, - grid_size); - fit.fit(scenario.observations); - - for (Eigen::Index i = 0; i < positions.size(); ++i) { - const double point = evaluation_point(scenario, positions(i)); - const double estimated_pdf = - fit.pdf(Eigen::VectorXd::Constant(1, point))(0); - const double estimated_cdf = - fit.cdf(Eigen::VectorXd::Constant(1, point))(0); - std::cout << scenario.name << ',' << scenario.scale << ',' << degree << ',' - << grid_size << ',' - << (std::isnan(bandwidth) ? "automatic" - : std::to_string(bandwidth)) - << ',' << positions(i) << ',' << point << ',' << estimated_pdf - << ',' << true_pdf(scenario.name, positions(i), scenario.scale) - << ',' << estimated_cdf << ',' - << true_cdf(scenario.name, positions(i)) << '\n'; - } -} - -} // namespace - -int -main() -{ - std::cout << std::setprecision(17); - std::cout << "scenario,scale,degree,grid_size,bandwidth,position,x," - "estimated_pdf,true_pdf,estimated_cdf,true_cdf\n"; - - Eigen::VectorXd positions(12); - positions << 0.0, 1e-12, 1e-10, 1e-8, 1e-6, 1e-5, 1e-4, 1e-3, - 1e-2, 1e-1, 0.5, 1.0; - const std::array scenario_names = { - "uniform", "beta-2-1", "beta-1-2", "exponential-left", - "exponential-right" - }; - - for (const std::string& scenario_name : scenario_names) { - for (double scale : { 1e-4, 1.0, 1e4 }) { - Scenario scenario = make_scenario(scenario_name, 2000, scale); - for (size_t degree = 0; degree < 3; ++degree) { - for (size_t grid_size : { 100, 400, 1000 }) { - for (double bandwidth : - { 0.15, 0.3, std::numeric_limits::quiet_NaN() }) { - run_scenario( - scenario, degree, grid_size, bandwidth, positions); - } - } - } - } - } -} diff --git a/diagnostic/one-sided-repair/HANDOFF.md b/diagnostic/one-sided-repair/HANDOFF.md deleted file mode 100644 index be19ba3..0000000 --- a/diagnostic/one-sided-repair/HANDOFF.md +++ /dev/null @@ -1,33 +0,0 @@ -# One-sided repair handoff - -The production branch already uses a scale-equivariant power-$3/4$ transform -for one-sided supports. The diagnostic candidate keeps that estimator as the -unweighted bulk and adds the selected two-boundary method's finite expert: -an averaged local-linear/local-quadratic kernel, a shrinking CDF weight, and a -$2\sqrt n$ order-statistic finite-versus-bulk decision. - -The native kernels share the degree-2 bandwidth fitted to the lowest 75% of -boundary distances. A 30-replication ablation compared fixed fractions from -15% through 100% and a $\sqrt n$ shrinking subset. Performance improved up to -75%; using all observations reversed the long-tail gains because remote Lomax -observations again controlled the floor. The 75% choice has mean global ISE -ratios to current of 0.902 at $n=100$ and 0.889 at $n=1000$, with corresponding -boundary ratios 0.854 and 0.834. - -The representative plots confirm that 75% removes most residual finite-endpoint -spiking. It is visually close to the full-sample floor for Exponential and -half-normal cases, but remains stable for Lomax. The main remaining loss is a -small-sample false finite classification for Gamma$(2)$: global ISE is 1.026 -and boundary ISE is 1.083 relative to current at $n=100$. At $n=1000$ the -classifier always chooses bulk for both Gamma examples, so the result is -exactly current. - -The log transform was rejected and removed. The working diagnostic now contains -only the current power-transform candidate and the floor-fraction validation. - -Before native C++ implementation, expand the scenario suite around the selected -75% value and classifier edge cases. In particular, add finite-boundary shapes -with steep nonzero slopes, heavier remote tails, upper-bounded reflections, and -sample sizes between 100 and 1000. Keep paired global/boundary ISE, bias, -variance, normalization, nonnegativity, reflection, scale, and realization -checks. diff --git a/diagnostic/one-sided-repair/NATIVE_CPP.md b/diagnostic/one-sided-repair/NATIVE_CPP.md deleted file mode 100644 index 3b9bdb2..0000000 --- a/diagnostic/one-sided-repair/NATIVE_CPP.md +++ /dev/null @@ -1,387 +0,0 @@ -# Native boundary-expert implementation roadmap - -## Scope - -Implement both selected finite-boundary repairs through one concise internal -path: - -| support | unchanged bulk estimator | candidate endpoints | bandwidth floor | -|---|---|---|---| -| exactly one finite endpoint | power-$3/4$ transform | the finite endpoint | closest 75% of boundary distances | -| two finite endpoints | probit transform | lower and upper, classified independently | all boundary distances | - -The existing transformed estimator remains the bulk component in both cases. -Unbounded continuous, discrete, and zero-inflated behavior remains unchanged. - -The production estimator activates for continuous fits of degrees zero through -two with at least 16 observations and effective sample size at least 16. Public -case weights and manual bandwidths are supported. Apply the bandwidth -multiplier to every expert bandwidth after selection and flooring. - -Expose boundary repair as a constructor option that defaults to enabled. When -disabled, retain the transformed bulk estimator. Do not add another fitted- -object representation. - -## Minimal integration point - -Call the repair coordinator only when `type_ == VarType::continuous`, at least -one support bound is finite, and at least 16 cleaned observations remain. The -coordinator additionally retains the bulk fit when the effective sample size is -below 16. - -Keep the current body of `Kde1d::fit()` through construction of the normalized -bulk `InterpolationGrid`. Preserve the cleaned observations on their original -scale before applying `boundary_transform()`. Immediately after constructing -the bulk grid: - -1. classify every finite endpoint from original-scale boundary distances; -2. return to the unchanged bulk path if no endpoint is confidently finite; -3. fit a boundary component only for each selected endpoint, using the existing - original-scale grid; -4. form endpoint weights from the normalized bulk CDF; -5. fuse bulk and selected endpoint values and replace `grid_` with the - normalized fused grid. - -The existing PDF, CDF, quantile, simulation, support truncation, and -log-likelihood code then operates on the fused grid. `bandwidth_` continues to -report the bulk bandwidth. - -Boundary distances and local densities can stay in the original units. Every -classifier ratio is dimensionless, and the boundary bandwidths -scale with the data, so this is equivalent to the R reference's affine map to -$[0,1]$ without adding a second normalization path. - -No changes should be required in `boundary_transform()`, `boundary_correct()`, -`construct_grid_points()`, `InterpolationGrid`, `PluginBandwidthSelector`, or -the public constructors. - -## Shared private helpers in `kde1d.hpp` - -Keep the implementation in the existing header and add three focused helpers. - -### 1. Endpoint classifier - -Given ascending distances from one endpoint, use -$k=\min(n-1,\lceil2\sqrt n\rceil)$ and - -$$ -\widehat\beta= -\frac{k}{\sum_{i=1}^k -\log\{d_{(k+1)}/\max(d_{(i)},\epsilon d_{(k+1)})\}}}. -$$ - -The scale-relative numerical floor preserves scale equivariance. Select the -finite expert when - -$$ -\widehat\beta\geq0.9, -\qquad -\widehat\beta\left\{1- -\frac{\Phi^{-1}(0.95)}{\sqrt{k}}\right\}\leq1. -$$ - -Run this helper once for the one-sided finite endpoint and independently on -lower and upper distances for two-sided support. Exploding, vanishing, and -ambiguous endpoints all select bulk. A nonpositive $(k+1)$st distance or a -nonfinite/nonpositive logarithmic denominator is a degenerate classifier input -and must also select bulk. - -### 2. Local-polynomial boundary component - -The helper takes boundary distances, ascending evaluation distances, rank -weights, a floor fraction, and degree one or two. - -- Select the weighted bandwidth with `PluginBandwidthSelector`. -- Select one unweighted degree-2 bandwidth from the closest - $\max(4,\lceil q n\rceil)$ distances, where $q=0.75$ for one-sided support - and $q=1$ for two-sided support. -- Share it between the degree-one and degree-two kernels, then apply the public - multiplier. Evaluate density contributions with equal observation weights - so the estimand remains the original density. - -Construct the equivalent-kernel coefficients as the first row of the inverse -truncated-normal moment matrix. Generate the moments with - -$$ -\mu_0(a)=\Phi(a),\qquad -\mu_1(a)=-\phi(a),\qquad -\mu_j(a)=(j-1)\mu_{j-2}(a)-a^{j-1}\phi(a). -$$ - -Use the explicit degree-one and degree-two determinants to avoid a dynamic -matrix inverse at every evaluation point. Average the two kernels before -fusion, clamp negative values, and return both the density and its influence -numerator for the EDF calculation described below. - -Evaluate directly only where the endpoint weight is nonzero. With ordered -distances, omit observations more than six bandwidths from an evaluation -point; the omitted Gaussian tail mass is below $2\times10^{-9}$. Normalize the -fused grid once at the end. - -### 3. Boundary-repair coordinator - -This helper owns endpoint distances, classification, local component calls, -CDF weights, reflection, and fusion. - -For an upper endpoint, compute on ascending reflected distances and reverse the -component once. The floor fraction is the only local-component policy that -differs between one- and two-sided support. - -The helper should return an empty result when every endpoint selects bulk. -`Kde1d::fit()` can then leave the already constructed bulk grid untouched. - -## Weights and fusion - -Let $F_B(x)$ be the bulk CDF and - -$$ -q_n=\min(0.25,n^{-1/2}), -\qquad -s(r)=3r^2-2r^3. -$$ - -For a lower endpoint use - -$$ -w_L(x)=1-s\left(\min\{1,F_B(x)/q_n\}\right), -$$ - -and for an upper endpoint use - -$$ -w_U(x)=1-s\left(\min\{1,(1-F_B(x))/q_n\}\right). -$$ - -Set the weight of every bulk-classified endpoint to zero. The final values are - -$$ -\widehat f(x)= -w_L(x)\widehat f_L(x) -+\{1-w_L(x)-w_U(x)\}\widehat f_B(x) -+w_U(x)\widehat f_U(x). -$$ - -With $q_n\leq0.25$, the endpoint weights do not overlap. The same expression -covers one-sided support by setting the absent endpoint weight to zero. Clamp -the fused values at zero and construct a normalized `InterpolationGrid` on the -existing original-scale grid. - -## Conditional EDF approximation - -The current EDF is already a conditional influence-trace approximation: it -holds the selected bandwidth and final grid normalization fixed. Extend the -same convention to expert selection and fusion rather than returning `NaN`. - -For a degree-$p$ boundary component, let $M_p(a)$ be the truncated-normal -moment matrix above, let $h$ be the shared bandwidth, and let -$\widetilde f_p$ denote its value before clamping. Its influence numerator is - -$$ -\nu_p(x)= -\mathbf 1\{\widetilde f_p(x)>0\} -\frac{\phi(0)}{n h} -\left[M_p\{d(x)/h\}^{-1}\right]_{00}. -$$ - -Only the constant equivalent-kernel coefficient remains because a -self-contribution has kernel argument zero. For the equal linear/quadratic -expert, use - -$$ -f_E(x)=\frac{f_1(x)+f_2(x)}{2}, -\qquad -\nu_E(x)=\frac{\nu_1(x)+\nu_2(x)}{2}. -$$ - -For the bulk component, the existing influence column is its log-density -leverage $\ell_B(x)$, so its influence numerator is -$\nu_B(x)=f_B(x)\ell_B(x)$. Fuse the numerators with exactly the same weights -as the densities: - -$$ -\begin{aligned} -g(x)&=w_L(x)f_L(x) - +\{1-w_L(x)-w_U(x)\}f_B(x)+w_U(x)f_U(x),\\ -\nu(x)&=w_L(x)\nu_L(x) - +\{1-w_L(x)-w_U(x)\}\nu_B(x)+w_U(x)\nu_U(x),\\ -\ell(x)&=\frac{\nu(x)}{g(x)}. -\end{aligned} -$$ - -Thus the mixture leverage is weighted by local density shares, not just by -the fusion weights. Estimate - -$$ -\operatorname{edf}=\sum_{i=1}^n -\min\{3,\max(0,\ell(X_i))\}, -$$ - -retaining the current per-observation cap. The final common normalization of -$g$ and $\nu$ cancels in their ratio when its derivative is ignored. - -This approximation conditions on bandwidths, endpoint classifications, CDF -weights, clamp states, and normalization constants. It deliberately omits the -derivatives of those data-adaptive choices. That keeps it consistent with the -existing EDF convention and costs only additional grid-vector arithmetic; no -refits or per-observation matrices are needed. Validate it diagnostically -against the corresponding leave-one-out approximation - -$$ -1+\sum_{i=1}^n -\{\log \widehat f(X_i)-\log \widehat f_{-i}(X_i)\}. -$$ - -First confirm that this diagnostic reproduces the existing bulk EDF to the -expected approximation error. A weight-derivative correction is worth -considering only if the active-expert comparison then shows an additional -systematic discrepancy. - -## Weights and remaining fit metadata - -Expert density contributions use the normalized public case weights, matching -the weighted bulk estimand. Effective sample size determines the minimum sample -check, fusion width, tail order, and classifier confidence. The weighted -classifier uses a conservative lower threshold of 0.975. The one-sided -bandwidth uses the closest 75% of positive-weight observations by row count and -passes their case weights to the plug-in selector. The influence numerator uses -the local average case weight on the FFT grid. - -Recompute `loglik_` from the final grid using the existing code. Use the -conditional mixture trace above for `edf_` whenever a finite expert is active, -and retain the current calculation unchanged for pure-bulk fits. - -No classifier choice, tail index, boundary bandwidth, or weight state needs to -persist in the fitted object for the first implementation. Diagnostic values -belong in tests and validation scripts rather than the public class layout. - -## Exact production changes - -The intended implementation footprint is: - -1. `include/kde1d/kde1d.hpp` - - preserve original-scale cleaned observations; - - add the three private helpers; - - call the coordinator after bulk-grid construction; - - carry the bulk and expert influence numerators through fusion for EDF. -2. `test/test.cpp` - - deterministic golden results and fallback behavior. -3. `test/test_numerical_invariants.cpp` - - active-expert normalization, reflection, scale, support, and quantile - invariants. -4. `diagnostic/one-sided-repair/` and `diagnostic/boundary-repair/` - - thin R evaluators and final baseline-versus-native reports. - -Avoid modifying `interpolation.hpp`, `dpik.hpp`, `stats.hpp`, constructors, or -public getters unless implementation evidence shows that it is necessary. - -## Implementation sequence - -1. Synchronize this branch with the isolated PR #34 fix so - `boundary_offset_` is `NaN` before fitting. Record the current production - head and run the native R evaluators once to create one- and two-sided - baseline outputs before changing estimator behavior. -2. Add the eligibility check and preserve original-scale observations. With - the coordinator returning bulk, verify tight numerical parity for every - existing support type. -3. Implement the shared endpoint classifier and deterministic finite/bulk - tests for lower and upper endpoints. -4. Implement the shared degree-one/two equivalent-kernel evaluator. Validate - both bandwidth-floor policies against the retained R references. -5. Activate one-sided fusion with the 75% floor and verify the selected - one-sided scenarios. -6. Activate two-sided fusion with the full-sample floor and verify independent - lower/upper decisions, including asymmetric densities. -7. Complete log-likelihood and conditional-EDF handling, numerical regression - tests, and fit-time benchmarks. -8. Run the larger R validation against the recorded native baselines, retain - only final comparison artifacts, and prepare the PR report. - -Each step should be a separately testable commit. Avoid refactoring unrelated -fit logic while implementing the method. - -## Weighted and manual-bandwidth resolution - -Manual bandwidths control only the transformed bulk fit. Boundary bandwidths -remain independently selected in original data units, exactly as when the bulk -bandwidth is automatic. The public multiplier remains the common smoothing -control and scales both bulk and expert bandwidths. - -Weighted experiments rejected defining the one-sided 75% bandwidth subset by -cumulative weight: concentrated weights made that subset too narrow and -unstable. Counting positive-weight observations was both simpler and more -accurate. Effective sample size gave a small but consistent improvement for the -fusion width under concentrated weights. A weighted classifier threshold of -0.975 avoided most false repair of exploding targets while retaining the -finite-boundary gains. Global weight rescaling and insertion or removal of -zero-weight observations are numerically invariant. - -Integer-weight replication equivalence is not required here because the -existing bulk bandwidth selector interprets public weights through effective -sample size rather than as frequency counts. Supporting frequency weights -would require a separate change to the bulk estimator's weight semantics. - -### Degrees zero and one - -The same averaged local-linear/local-quadratic boundary expert is used for all -three bulk degrees. It outperformed matching-order and local-linear-only -alternatives in global and boundary ISE. The gains persisted for weighted and -manual-bandwidth fits, and boundary scale equivariance is tested for every -degree. Degree zero primarily trades substantially lower boundary bias for a -small one-sided variance increase; degree one reduces both bias and variance. - -## Native tests - -Add compact tests to the existing executables. - -Shared coverage: - -- nonnegativity, unit mass, monotone CDF, quantile round trips, finite - log-likelihood and EDF, and support truncation; -- exact EDF parity with the current path when no expert is active, plus - diagnostic comparison with leave-one-out log-likelihood optimism when an - expert is active; -- scaling over several orders of magnitude; -- ties, observations exactly at an endpoint, small samples, and nearly - degenerate samples; -- regression coverage for unbounded, discrete, zero-inflated, weighted, - fixed-bandwidth, and nondefault-degree fits; -- fit-time benchmarks at representative $n$ values. - -One-sided coverage: - -- deterministic Exponential, half-normal, Gamma$(2)$, Gamma$(0.75)$, and - Lomax samples; -- lower/upper reflection while the expert is active; -- finite and bulk classifier outcomes; -- golden grid or PDF values against `one_sided_estimator.R`. - -Two-sided coverage: - -- deterministic Uniform, Beta$(1,2)$, Beta$(0.75,2)$, and - Beta$(0.75,0.75)$ samples; -- lower and upper finite/bulk outcomes, including asymmetric decisions; -- affine equivariance on non-unit intervals; -- golden grid or PDF values against `bounded_estimator.R`. - -If direct local evaluation is materially expensive, optimize only after a -profile identifies it as the relevant fit cost. - -## R validation without C++ experiment bloat - -Keep Monte Carlo comparisons in R. Use small native-evaluator scripts that run -the installed estimator for deterministic scenario seeds and write -replication-level global and boundary ISE plus aggregate squared bias and -variance. Run them once at the recorded baseline commit and once at the -candidate commit, then join the outputs in reporting scripts. - -This avoids a legacy-mode switch in the public C++ API and avoids maintaining -two production estimator paths solely for benchmarking. - -The final one-sided suite should expand the retained scenarios with -intermediate sample sizes, steeper finite-endpoint slopes, heavier remote -tails, upper-bounded reflections, and visual realizations. The final two-sided -suite should retain varied symmetric and asymmetric finite, vanishing, and -exploding endpoint shapes plus local boundary plots. Report paired ISE ratios -with Monte Carlo uncertainty, global and local bias/variance, classifier rates -computed by matching R code, visual examples, and fit time relative to the -current transformed baselines. diff --git a/diagnostic/one-sided-repair/README.md b/diagnostic/one-sided-repair/README.md deleted file mode 100644 index 41b2b56..0000000 --- a/diagnostic/one-sided-repair/README.md +++ /dev/null @@ -1,46 +0,0 @@ -# One-sided boundary repair - -This workspace applies the selected two-boundary idea to continuous densities -with exactly one known finite endpoint. It is deliberately separate from -`boundary-repair/`, which is stable. - -## Current candidate - -The power-$3/4$ transformation estimator is the unweighted bulk fit. A single -order-statistic tail index classifies the finite endpoint using -$k=\min(n-1,\lceil2\sqrt n\rceil)$ and the same 95% rule as in the -two-boundary estimator. A confidently finite endpoint receives the averaged -local-linear/local-quadratic kernel expert; exploding, vanishing, and ambiguous -endpoints reuse bulk. - -The boundary expert is blended with bulk through a smooth weight based on the -bulk CDF, with boundary probability $\min(0.25,n^{-1/2})$. Both kernels share -the degree-2 bandwidth fitted to the closest 75% of boundary distances. The -native evaluator only computes expert values where this weight is nonzero and -normalizes once after fusion. This preserves the stabilizing information in -most of the sample without allowing the most remote observations to dominate. -The construction is reflection- and scale-equivariant. - -The validation suite uses 30 paired replications at $n=100,1000$ for -Exponential, half-normal, Gamma$(2)$, Gamma$(0.75)$, and Lomax$(2)$ densities. -The log transform was rejected and its experimental implementation and outputs -have been removed. - -## Files - -- `scripts/one_sided_estimator.R`: pre-native tuning implementation. -- `scripts/ablate_local_floor_fraction.R`: selected floor-fraction ablation. -- `scripts/plot_local_floor_fraction_ablation.R`: tuning curves and example - estimates. -- `results/local-floor-fraction-ablation.csv` and - `plots/local-floor-fraction-ablation.pdf`: current tuning evidence. -- `RESULTS.md`: numerical conclusions. -- `HANDOFF.md`: implementation state and next steps. -- `NATIVE_CPP.md`: shared one- and two-sided native implementation roadmap. - -Run from the R-package root: - -```sh -Rscript inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R 30 -Rscript inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R -``` diff --git a/diagnostic/one-sided-repair/RESULTS.md b/diagnostic/one-sided-repair/RESULTS.md deleted file mode 100644 index b302222..0000000 --- a/diagnostic/one-sided-repair/RESULTS.md +++ /dev/null @@ -1,59 +0,0 @@ -# One-sided boundary-repair results - -## Estimator held fixed during the ablation - -The candidate uses the power-$3/4$ estimator as unweighted bulk. If the -order-statistic classifier identifies a finite nonzero endpoint, equal -local-linear and local-quadratic estimates are blended into the shrinking -boundary region. Only the bandwidth-floor sample fraction changes. - -The experiment uses 30 paired replications for five densities at $n=100$ and -$n=1000$. It compares the lowest 15%, 20%, 25%, 30%, 35%, 40%, 50%, 75%, and -100% of boundary distances, plus a shrinking subset of $\lceil\sqrt n\rceil$ -distances. All values below are candidate/current ratios, so smaller is better. - -## Aggregate result - -| $n$ | floor subset | global ISE | boundary ISE | squared bias | variance | -|---:|---:|---:|---:|---:|---:| -| 100 | 25% | 0.989 | 0.986 | 0.895 | 1.007 | -| 100 | 50% | 0.933 | 0.899 | 0.860 | 0.949 | -| 100 | 75% | **0.902** | **0.854** | **0.829** | **0.917** | -| 100 | 100% | 0.941 | 0.911 | 1.004 | 0.923 | -| 100 | $\sqrt n$ | 1.073 | 1.127 | 0.905 | 1.102 | -| 1000 | 25% | 0.933 | 0.896 | 0.801 | 0.976 | -| 1000 | 50% | 0.909 | 0.863 | 0.797 | 0.946 | -| 1000 | 75% | **0.889** | **0.834** | **0.789** | **0.924** | -| 1000 | 100% | 0.983 | 0.959 | 0.963 | 0.986 | -| 1000 | $\sqrt n$ | 1.043 | 1.064 | 0.806 | 1.112 | - -The old 25% floor is too local. Increasing the subset through 75% reduces both -bias and variance. A shrinking $\sqrt n$ subset is clearly too small and -reintroduces instability. Using the full sample overshoots the optimum because -remote tail observations again inflate the floor. - -## Selected 75% floor by density - -| density | $n$ | global ISE | boundary ISE | squared bias | variance | -|---|---:|---:|---:|---:|---:| -| Exponential | 100 | 0.808 | 0.709 | 0.575 | 0.841 | -| Exponential | 1000 | 0.805 | 0.722 | 0.455 | 0.890 | -| half-normal | 100 | 0.869 | 0.744 | 0.817 | 0.878 | -| half-normal | 1000 | 0.808 | 0.672 | 0.868 | 0.801 | -| Gamma$(2)$ | 100 | 1.026 | 1.083 | 1.174 | 1.019 | -| Gamma$(2)$ | 1000 | 1.000 | 1.000 | 1.000 | 1.000 | -| Gamma$(0.75)$ | 100 | 0.985 | 0.983 | 0.913 | 0.992 | -| Gamma$(0.75)$ | 1000 | 1.000 | 1.000 | 1.000 | 1.000 | -| Lomax$(2)$ | 100 | 0.819 | 0.752 | 0.670 | 0.857 | -| Lomax$(2)$ | 1000 | 0.833 | 0.774 | 0.622 | 0.926 | - -The full-sample floor would improve the finite light-tail cases further, but it -raises Lomax global ISE to 1.075 at $n=100$ and 1.392 at $n=1000$. The 75% -floor retains large improvements for both light and long remote tails and is -therefore the selected default. - -The realization plots show the same trade-off. Relative to 25%, the selected -floor substantially calms the near-endpoint estimates. Relative to 100%, it -avoids the flattened Lomax boundary while remaining visually smooth for -Exponential data. 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b/diagnostic/one-sided-repair/results/local-floor-fraction-ablation.csv deleted file mode 100644 index 9aebb6c..0000000 --- a/diagnostic/one-sided-repair/results/local-floor-fraction-ablation.csv +++ /dev/null @@ -1,111 +0,0 @@ -"distribution","sample_size","replications","method","global_ise","global_squared_bias","global_variance","boundary_ise","boundary_squared_bias","boundary_variance","finite_rate","mean_floor_ratio","minimum_density","maximum_mass_error" -"exponential",100,30,"current",0.0165472389855547,0.00205016560497188,0.0144970733805828,0.0106234994208158,0.00126599700538637,0.00935750241542941,NA,NA,1.87620764495024e-15,1.11022302462516e-16 -"exponential",100,30,"fixed-15pct",0.0164068280322217,0.00176173524182124,0.0146450927904004,0.0104884088522769,0.000969273783595678,0.00951913506868119,0.666666666666667,2.26138933228023,0,1.11022302462516e-16 -"exponential",100,30,"fixed-20pct",0.0157245002505956,0.00165925024528034,0.0140652500053152,0.00977827871653413,0.000871272403187169,0.00890700631334696,0.666666666666667,2.72230964287038,1.8683320459021e-15,1.11022302462516e-16 -"exponential",100,30,"fixed-25pct",0.0154464207902959,0.00159454865963953,0.0138518721306564,0.0094772157298769,0.00081402806341869,0.00866318766645821,0.666666666666667,3.3746911588894,1.86756569172953e-15,1.11022302462516e-16 -"exponential",100,30,"fixed-30pct",0.0152787565880896,0.00159907933870905,0.0136796772493806,0.00929504572248738,0.000818405451515906,0.00847664027097147,0.666666666666667,4.09079193231902,1.87053078117119e-15,1.11022302462516e-16 -"exponential",100,30,"fixed-35pct",0.0150985550244765,0.00157889875105775,0.0135196562734187,0.00910619553077884,0.00080019644459805,0.00830599908618079,0.666666666666667,4.74814780644128,1.87467719387415e-15,1.11022302462516e-16 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-"gamma_0.75",1000,30,"fixed-30pct",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"gamma_0.75",1000,30,"fixed-35pct",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"gamma_0.75",1000,30,"fixed-40pct",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"gamma_0.75",1000,30,"fixed-50pct",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"gamma_0.75",1000,30,"fixed-75pct",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"gamma_0.75",1000,30,"fixed-100pct",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"gamma_0.75",1000,30,"shrinking",0.00800935397940015,0.00240562435989908,0.00560372961950107,0.00685770784468224,0.00230260733820975,0.00455510050647249,0,NA,2.36840057628249e-09,1.11022302462516e-16 -"lomax_2",100,30,"current",0.0320268987246898,0.00648388858700561,0.0255430101376842,0.022571498829797,0.00539273643819479,0.0171787623916022,NA,NA,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-15pct",0.0341784289040103,0.00545431820112166,0.0287241107028886,0.0246692629391396,0.00437317194694695,0.0202960909921927,0.7,1.74298292023704,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-20pct",0.0329364272846334,0.00531565631751246,0.0276207709671209,0.0234373427192617,0.00422860716891606,0.0192087355503456,0.7,2.25345608974253,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-25pct",0.0315504362882948,0.00516885482754763,0.0263815814607472,0.022037140835904,0.00407275491685668,0.0179643859190473,0.7,2.77239130253995,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-30pct",0.0302487831990908,0.00501418054191126,0.0252346026571795,0.0207106798807081,0.00390287366269442,0.0168078062180136,0.7,3.42851685390775,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-35pct",0.0299454664033389,0.00498769968054349,0.0249577667227954,0.0204190781644711,0.00387799504835325,0.0165410831161179,0.7,4.08323232164168,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-40pct",0.0294528981772044,0.00493738819233153,0.0245155099848729,0.0199445389599459,0.00382085750427208,0.0161236814556738,0.7,4.72644379724695,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-50pct",0.0285189100946901,0.00474155087942755,0.0237773592152626,0.0190556289633984,0.00360673315380207,0.0154488958095963,0.7,6.18958080513734,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-75pct",0.0262364414943695,0.00434160891191695,0.0218948325824526,0.0169627470963472,0.00315960086719081,0.0138031462291564,0.7,11.9477658059949,0,1.11022302462516e-16 -"lomax_2",100,30,"fixed-100pct",0.0344264830854107,0.0101608357551471,0.0242656473302637,0.0250325446664152,0.00909821530212285,0.0159343293642923,0.7,92.7046182399041,0,1.11022302462516e-16 -"lomax_2",100,30,"shrinking",0.0349986902781772,0.0053166941988258,0.0296819960793514,0.0255221859554241,0.00423518037423045,0.0212870055811936,0.7,1.33704272336928,0,1.11022302462516e-16 -"lomax_2",1000,30,"current",0.00466466138729923,0.00143513707469976,0.00322952431259947,0.00350149716851033,0.00112671300315472,0.00237478416535561,NA,NA,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-15pct",0.00436099990888606,0.000878121257830974,0.00348287865105509,0.00320092795758196,0.000564160869336452,0.00263676708824551,0.666666666666667,4.4932550558715,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-20pct",0.00423966119040754,0.000876618726807714,0.00336304246359983,0.00307622311705505,0.000560854659297538,0.00251536845775752,0.666666666666667,5.81675470465849,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-25pct",0.0041430445540767,0.000876082849395204,0.0032669617046815,0.00297729161922663,0.00055846411536554,0.00241882750386109,0.666666666666667,7.11933483971629,0,2.22044604925031e-16 -"lomax_2",1000,30,"fixed-30pct",0.0040731577359026,0.000877330147025215,0.00319582758887738,0.00290481115181225,0.00055813996746545,0.0023466711843468,0.666666666666667,8.52294235352961,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-35pct",0.00401937859112426,0.000878730832829979,0.00314064775829428,0.00284942159321027,0.000558245311673399,0.00229117628153687,0.666666666666667,9.97469592167928,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-40pct",0.00397052028672156,0.000880354759175136,0.00309016552754642,0.0027996394210534,0.00055854532208646,0.00224109409896694,0.666666666666667,11.5527001556363,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-50pct",0.00390556519468693,0.000885414325502173,0.00302015086918476,0.00273302688240551,0.000561236325944702,0.0021717905564608,0.666666666666667,15.168288605388,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-75pct",0.00388389723608418,0.000892559922975234,0.00299133731310895,0.00271109831571414,0.000567744771275972,0.00214335354443817,0.666666666666667,28.0685793643946,0,1.11022302462516e-16 -"lomax_2",1000,30,"fixed-100pct",0.00649334812218761,0.00215366087792471,0.0043396872442629,0.00536551738685692,0.00189185791667889,0.00347365947017803,0.666666666666667,316.351208853879,0,1.11022302462516e-16 -"lomax_2",1000,30,"shrinking",0.00485525856366109,0.000865000667250043,0.00399025789641104,0.00369570145755347,0.000550680684486621,0.00314502077306685,0.666666666666667,1.32912073570791,0,1.11022302462516e-16 diff --git a/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R b/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R deleted file mode 100644 index ec0bd78..0000000 --- a/diagnostic/one-sided-repair/scripts/ablate_local_floor_fraction.R +++ /dev/null @@ -1,212 +0,0 @@ -# Paired ablation of the local probability mass used for the bandwidth floor. -# Run from the root of the kde1d R package. - -if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { - stop("run from the kde1d package root with pkgload installed") -} -pkgload::load_all(".", quiet = TRUE) -source(paste0( - "inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/", - "one_sided_estimator.R" -)) - -arguments <- commandArgs(trailingOnly = TRUE) -replication_count <- if (length(arguments) >= 1L) { - as.integer(arguments[[1L]]) -} else { - 30L -} -output_file <- if (length(arguments) >= 2L) arguments[[2L]] else paste0( - "inst/include/kde1d-cpp/diagnostic/one-sided-repair/results/", - "local-floor-fraction-ablation.csv" -) -if (length(arguments) > 2L || !is.finite(replication_count) || - replication_count < 2L) { - stop("usage: ablate_local_floor_fraction.R [replications] [output.csv]") -} - -validation_distributions <- list( - exponential = list(random = rexp, density = dexp, quantile = qexp), - half_normal = list( - random = function(sample_size) abs(rnorm(sample_size)), - density = function(values) 2 * dnorm(values), - quantile = function(probabilities) qnorm((probabilities + 1) / 2) - ), - gamma_2 = list( - random = function(sample_size) rgamma(sample_size, 2), - density = function(values) dgamma(values, 2), - quantile = function(probabilities) qgamma(probabilities, 2) - ), - gamma_0.75 = list( - random = function(sample_size) rgamma(sample_size, 0.75), - density = function(values) dgamma(values, 0.75), - quantile = function(probabilities) qgamma(probabilities, 0.75) - ), - lomax_2 = list( - random = function(sample_size) (1 - runif(sample_size))^(-0.5) - 1, - density = function(values) 2 / (1 + values)^3, - quantile = function(probabilities) (1 - probabilities)^(-0.5) - 1 - ) -) -sample_sizes <- c(100L, 1000L) -local_floor_fractions <- c( - 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.50, 0.75, 1 -) -fraction_methods <- paste0( - "fixed-", - format(100 * local_floor_fractions, trim = TRUE), - "pct" -) -candidate_methods <- c(fraction_methods, "shrinking") -methods <- c("current", candidate_methods) -evaluation_probabilities <- sort(unique(c( - 10^seq(-10, -2, length.out = 101L), - seq(0.01, 0.999, length.out = 401L), - 0.9999, 0.99999 -))) -result_rows <- list() - -summarize_fraction_estimates <- function( - evaluation_points, - estimates, - true_density, - region_points) { - mean_density <- rowMeans(estimates) - integrated_errors <- vapply(seq_len(ncol(estimates)), function(replication) { - one_sided_trapezoid_integral( - evaluation_points[region_points], - (estimates[region_points, replication] - true_density[region_points])^2 - ) - }, numeric(1L)) - c( - ise = mean(integrated_errors), - squared_bias = one_sided_trapezoid_integral( - evaluation_points[region_points], - (mean_density[region_points] - true_density[region_points])^2 - ), - variance = one_sided_trapezoid_integral( - evaluation_points[region_points], - rowMeans((estimates[region_points, , drop = FALSE] - - mean_density[region_points])^2) - ) - ) -} - -for (distribution_index in seq_along(validation_distributions)) { - evaluation_points <- validation_distributions[[distribution_index]]$quantile( - evaluation_probabilities - ) - true_density <- validation_distributions[[distribution_index]]$density( - evaluation_points - ) - boundary_points <- evaluation_probabilities <= 0.1 - for (sample_size in sample_sizes) { - estimates <- setNames(lapply(methods, function(method) { - matrix(NA_real_, length(evaluation_points), replication_count) - }), methods) - finite_choices <- logical(replication_count) - floor_ratios <- setNames(lapply(candidate_methods, function(method) { - rep(NA_real_, replication_count) - }), candidate_methods) - for (replication in seq_len(replication_count)) { - set.seed( - 20260914L + 100000L * distribution_index + - 1000L * match(sample_size, sample_sizes) + replication - ) - observations <- validation_distributions[[distribution_index]]$random( - sample_size - ) - estimates$current[, replication] <- normalize_one_sided_density( - evaluation_points, - dkde1d(evaluation_points, kde1d(observations, xmin = 0)) - ) - for (fraction_index in seq_along(local_floor_fractions)) { - method <- fraction_methods[[fraction_index]] - candidate_fit <- fit_one_sided_candidate( - observations, - evaluation_points, - bandwidth_floor = "local", - local_floor_fraction = local_floor_fractions[[fraction_index]] - ) - estimates[[method]][, replication] <- candidate_fit$density - floor_ratios[[method]][[replication]] <- mean( - candidate_fit$boundary_bandwidths / - candidate_fit$selected_boundary_bandwidths - ) - if (fraction_index == 1L) { - finite_choices[[replication]] <- - candidate_fit$expert_choice == "finite" - } - } - shrinking_fit <- fit_one_sided_candidate( - observations, - evaluation_points, - bandwidth_floor = "shrinking" - ) - estimates$shrinking[, replication] <- shrinking_fit$density - floor_ratios$shrinking[[replication]] <- mean( - shrinking_fit$boundary_bandwidths / - shrinking_fit$selected_boundary_bandwidths - ) - } - for (method in methods) { - global_summary <- summarize_fraction_estimates( - evaluation_points, - estimates[[method]], - true_density, - rep(TRUE, length(evaluation_points)) - ) - boundary_summary <- summarize_fraction_estimates( - evaluation_points, - estimates[[method]], - true_density, - boundary_points - ) - result_rows[[length(result_rows) + 1L]] <- data.frame( - distribution = names(validation_distributions)[[distribution_index]], - sample_size = sample_size, - replications = replication_count, - method = method, - global_ise = global_summary[["ise"]], - global_squared_bias = global_summary[["squared_bias"]], - global_variance = global_summary[["variance"]], - boundary_ise = boundary_summary[["ise"]], - boundary_squared_bias = boundary_summary[["squared_bias"]], - boundary_variance = boundary_summary[["variance"]], - finite_rate = if (method %in% candidate_methods) { - mean(finite_choices) - } else { - NA_real_ - }, - mean_floor_ratio = if ( - method %in% candidate_methods && - any(is.finite(floor_ratios[[method]])) - ) { - mean(floor_ratios[[method]], na.rm = TRUE) - } else { - NA_real_ - }, - minimum_density = min(estimates[[method]]), - maximum_mass_error = max(abs(vapply( - seq_len(replication_count), - function(replication) { - one_sided_trapezoid_integral( - evaluation_points, - estimates[[method]][, replication] - ) - 1 - }, - numeric(1L) - ))) - ) - } - message( - names(validation_distributions)[[distribution_index]], - ", n = ", sample_size - ) - } -} - -results <- do.call(rbind, result_rows) -dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) -write.csv(results, output_file, row.names = FALSE) -message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/one-sided-repair/scripts/one_sided_estimator.R b/diagnostic/one-sided-repair/scripts/one_sided_estimator.R deleted file mode 100644 index 8a9ec0b..0000000 --- a/diagnostic/one-sided-repair/scripts/one_sided_estimator.R +++ /dev/null @@ -1,360 +0,0 @@ -# Reference R implementation of the one-sided finite-boundary candidate. - -one_sided_trapezoid_integral <- function(evaluation_points, values) { - sum(diff(evaluation_points) * - (values[-length(values)] + values[-1L]) / 2) -} - -normalize_one_sided_density <- function(evaluation_points, density) { - density <- pmax(0, density) - density_mass <- one_sided_trapezoid_integral(evaluation_points, density) - if (!is.finite(density_mass) || density_mass <= 0) { - stop("density cannot be normalized") - } - density / density_mass -} - -one_sided_smoothstep <- function(normalized_distance) { - 3 * normalized_distance^2 - 2 * normalized_distance^3 -} - -make_one_sided_expert_weights <- function(probabilities, sample_size, - concentration = 1, - shrinkage_exponent = 0.5) { - boundary_fraction <- min( - 0.25, - concentration / sample_size^shrinkage_exponent - ) - boundary_weights <- 1 - one_sided_smoothstep(pmin( - 1, - probabilities / boundary_fraction - )) - cbind(boundary = boundary_weights, bulk = 1 - boundary_weights) -} - -one_sided_weighted_quantile <- function(values, weights, probability) { - value_order <- order(values) - ordered_weights <- weights[value_order] - values[value_order][which( - cumsum(ordered_weights) / sum(ordered_weights) >= probability - )[[1L]]] -} - -select_one_sided_bandwidth_floor <- function( - boundary_distances, - bandwidth_weights, - degree, - bandwidth_floor = c("local", "shrinking", "global", "none", "robust"), - local_floor_fraction = 0.75) { - bandwidth_floor <- match.arg(bandwidth_floor) - if (bandwidth_floor == "none") { - return(0) - } - if (bandwidth_floor == "global") { - return(kde1d(boundary_distances, deg = degree)$bw) - } - if (bandwidth_floor == "local" || bandwidth_floor == "shrinking") { - if (!is.finite(local_floor_fraction) || local_floor_fraction <= 0 || - local_floor_fraction > 1) { - stop("local_floor_fraction must lie in (0, 1]") - } - local_count <- if (bandwidth_floor == "shrinking") { - max(4L, ceiling(sqrt(length(boundary_distances)))) - } else { - max(4L, ceiling(local_floor_fraction * length(boundary_distances))) - } - return(kde1d(sort(boundary_distances)[seq_len(local_count)], deg = degree)$bw) - } - weighted_median <- one_sided_weighted_quantile( - boundary_distances, - bandwidth_weights, - 0.5 - ) - weighted_mad <- one_sided_weighted_quantile( - abs(boundary_distances - weighted_median), - bandwidth_weights, - 0.5 - ) - if (!(weighted_mad > 0)) { - weighted_mad <- one_sided_weighted_quantile( - boundary_distances, - bandwidth_weights, - 0.75 - ) - weighted_median - } - if (!(weighted_mad > 0)) { - weighted_mad <- max(boundary_distances) * .Machine$double.eps - } - winsorized_distances <- pmin( - boundary_distances, - weighted_median + 6 * weighted_mad - ) - kde1d(winsorized_distances, deg = degree)$bw -} - -fit_one_sided_bulk <- function( - observations, - evaluation_points, - lower_bound, - upper_bound) { - lower_bounded <- !is.na(lower_bound) - bulk_model <- if (lower_bounded) { - kde1d(observations, xmin = lower_bound) - } else { - kde1d(observations, xmax = upper_bound) - } - list( - density = normalize_one_sided_density( - evaluation_points, - dkde1d(evaluation_points, bulk_model) - ), - boundary_probabilities = if (lower_bounded) { - pkde1d(evaluation_points, bulk_model) - } else { - 1 - pkde1d(evaluation_points, bulk_model) - } - ) -} - -fit_one_sided_local_polynomial <- function( - boundary_distances, - evaluation_distances, - bandwidth_weights, - minimum_bandwidth, - degree) { - if (!degree %in% c(1, 2)) { - stop("local boundary degree must be 1 or 2") - } - selected_bandwidth <- kde1d( - boundary_distances, - weights = bandwidth_weights, - deg = degree - )$bw - bandwidth <- max(selected_bandwidth, minimum_bandwidth) - standardized_boundary <- evaluation_distances / bandwidth - truncated_moment_0 <- pnorm(standardized_boundary) - truncated_moment_1 <- -dnorm(standardized_boundary) - truncated_moment_2 <- truncated_moment_0 - - standardized_boundary * dnorm(standardized_boundary) - if (degree == 1) { - moment_determinant <- truncated_moment_0 * truncated_moment_2 - - truncated_moment_1^2 - equivalent_kernel_coefficients <- cbind( - truncated_moment_2 / moment_determinant, - -truncated_moment_1 / moment_determinant - ) - } else { - truncated_moment_3 <- -( - standardized_boundary^2 + 2 - ) * dnorm(standardized_boundary) - truncated_moment_4 <- 3 * truncated_moment_0 - ( - standardized_boundary^3 + 3 * standardized_boundary - ) * dnorm(standardized_boundary) - moment_determinant <- - truncated_moment_0 * ( - truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 - ) - - truncated_moment_1 * ( - truncated_moment_1 * truncated_moment_4 - - truncated_moment_2 * truncated_moment_3 - ) + - truncated_moment_2 * ( - truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 - ) - equivalent_kernel_coefficients <- cbind( - ( - truncated_moment_2 * truncated_moment_4 - truncated_moment_3^2 - ) / moment_determinant, - ( - truncated_moment_2 * truncated_moment_3 - - truncated_moment_1 * truncated_moment_4 - ) / moment_determinant, - ( - truncated_moment_1 * truncated_moment_3 - truncated_moment_2^2 - ) / moment_determinant - ) - } - density <- numeric(length(evaluation_distances)) - for (chunk_start in seq(1L, length(evaluation_distances), by = 128L)) { - chunk_indices <- chunk_start:min( - chunk_start + 127L, - length(evaluation_distances) - ) - kernel_arguments <- outer( - evaluation_distances[chunk_indices], - boundary_distances, - "-" - ) / bandwidth - base_kernels <- dnorm(kernel_arguments) - corrected_kernels <- base_kernels * - equivalent_kernel_coefficients[chunk_indices, 1L] - for (polynomial_order in seq_len(degree)) { - corrected_kernels <- corrected_kernels + - base_kernels * - equivalent_kernel_coefficients[ - chunk_indices, - polynomial_order + 1L - ] * kernel_arguments^polynomial_order - } - density[chunk_indices] <- rowMeans(corrected_kernels) / bandwidth - } - list( - density = normalize_one_sided_density(evaluation_distances, density), - bandwidth = bandwidth, - selected_bandwidth = selected_bandwidth - ) -} - -select_one_sided_endpoint_expert <- function( - boundary_distances, - tail_multiplier = 2, - evidence_threshold = qnorm(0.95), - minimum_finite_index = 0.9) { - tail_count <- min( - length(boundary_distances) - 1L, - ceiling(tail_multiplier * sqrt(length(boundary_distances))) - ) - ordered_distances <- sort(boundary_distances) - tail_index <- tail_count / sum(log( - ordered_distances[[tail_count + 1L]] / - pmax(.Machine$double.eps, ordered_distances[seq_len(tail_count)]) - )) - list( - expert_choice = if ( - tail_index >= minimum_finite_index && - tail_index * (1 - evidence_threshold / sqrt(tail_count)) <= 1 - ) { - "finite" - } else { - "bulk" - }, - tail_index = tail_index, - tail_count = tail_count - ) -} - -fit_one_sided_candidate <- function( - observations, - evaluation_points, - lower_bound = 0, - upper_bound = NA_real_, - concentration = 1, - shrinkage_exponent = 0.5, - bandwidth_floor = c("local", "shrinking", "global", "none", "robust"), - local_floor_fraction = 0.75) { - bandwidth_floor <- match.arg(bandwidth_floor) - if (is.na(lower_bound) == is.na(upper_bound)) { - stop("exactly one finite boundary must be supplied") - } - if (length(observations) < 4L || any(!is.finite(observations)) || - any(!is.finite(evaluation_points)) || - is.unsorted(evaluation_points, strictly = TRUE)) { - stop("observations and evaluation_points must be finite and ordered") - } - lower_bounded <- !is.na(lower_bound) - boundary_distances <- if (lower_bounded) { - observations - lower_bound - } else { - upper_bound - observations - } - if (any(boundary_distances < 0)) { - stop("observations must lie inside the supplied support") - } - evaluation_distances <- if (lower_bounded) { - evaluation_points - lower_bound - } else { - rev(upper_bound - evaluation_points) - } - bulk_fit <- fit_one_sided_bulk( - observations, - evaluation_points, - lower_bound, - upper_bound - ) - selection <- select_one_sided_endpoint_expert(boundary_distances) - if (selection$expert_choice == "bulk") { - return(list( - density = bulk_fit$density, - expert_choice = "bulk", - tail_index = selection$tail_index, - tail_count = selection$tail_count, - boundary_bandwidths = c(linear = NA_real_, quadratic = NA_real_), - selected_boundary_bandwidths = c( - linear = NA_real_, quadratic = NA_real_ - ), - bandwidth_floor = bandwidth_floor, - local_floor_fraction = local_floor_fraction, - boundary_fraction = min( - 0.25, - concentration / length(observations)^shrinkage_exponent - ) - )) - } - probability_ranks <- (rank( - boundary_distances, - ties.method = "average" - ) - 0.5) / length(observations) - bandwidth_weights <- make_one_sided_expert_weights( - probability_ranks, - length(observations), - concentration, - shrinkage_exponent - )[, "boundary"] - local_fits <- lapply(c(1L, 2L), function(degree) { - fit_one_sided_local_polynomial( - boundary_distances, - evaluation_distances, - bandwidth_weights, - select_one_sided_bandwidth_floor( - boundary_distances, - bandwidth_weights, - degree, - bandwidth_floor, - local_floor_fraction - ), - degree - ) - }) - boundary_density <- rowMeans(vapply( - local_fits, - function(local_fit) local_fit$density, - numeric(length(evaluation_distances)) - )) - if (!lower_bounded) { - boundary_density <- rev(boundary_density) - } - evaluation_weights <- make_one_sided_expert_weights( - bulk_fit$boundary_probabilities, - length(observations), - concentration, - shrinkage_exponent - ) - list( - density = normalize_one_sided_density( - evaluation_points, - evaluation_weights[, "boundary"] * boundary_density + - evaluation_weights[, "bulk"] * bulk_fit$density - ), - expert_choice = "finite", - tail_index = selection$tail_index, - tail_count = selection$tail_count, - boundary_bandwidths = setNames( - vapply(local_fits, function(local_fit) local_fit$bandwidth, numeric(1L)), - c("linear", "quadratic") - ), - selected_boundary_bandwidths = setNames( - vapply( - local_fits, - function(local_fit) local_fit$selected_bandwidth, - numeric(1L) - ), - c("linear", "quadratic") - ), - bandwidth_floor = bandwidth_floor, - local_floor_fraction = local_floor_fraction, - boundary_fraction = min( - 0.25, - concentration / length(observations)^shrinkage_exponent - ) - ) -} diff --git a/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R b/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R deleted file mode 100644 index ce84da5..0000000 --- a/diagnostic/one-sided-repair/scripts/plot_local_floor_fraction_ablation.R +++ /dev/null @@ -1,163 +0,0 @@ -# Plot the local bandwidth-floor fraction ablation. -# Run from the root of the kde1d R package. - -if (!requireNamespace("pkgload", quietly = TRUE) || !file.exists("DESCRIPTION")) { - stop("run from the kde1d package root with pkgload installed") -} -pkgload::load_all(".", quiet = TRUE) -source(paste0( - "inst/include/kde1d-cpp/diagnostic/one-sided-repair/scripts/", - "one_sided_estimator.R" -)) - -input_file <- paste0( - "inst/include/kde1d-cpp/diagnostic/one-sided-repair/results/", - "local-floor-fraction-ablation.csv" -) -output_file <- paste0( - "inst/include/kde1d-cpp/diagnostic/one-sided-repair/plots/", - "local-floor-fraction-ablation.pdf" -) -results <- read.csv(input_file) -fractions <- as.numeric(sub( - "pct$", "", sub("fixed-", "", results$method[grepl("^fixed", results$method)]), - fixed = FALSE -)) -fractions <- sort(unique(fractions)) -comparison_distributions <- list( - exponential = list(random = rexp, density = dexp, quantile = qexp), - gamma_2 = list( - random = function(sample_size) rgamma(sample_size, 2), - density = function(values) dgamma(values, 2), - quantile = function(probabilities) qgamma(probabilities, 2) - ), - lomax_2 = list( - random = function(sample_size) (1 - runif(sample_size))^(-0.5) - 1, - density = function(values) 2 / (1 + values)^3, - quantile = function(probabilities) (1 - probabilities)^(-0.5) - 1 - ) -) -evaluation_probabilities <- sort(unique(c( - 10^seq(-10, -2, length.out = 101L), - seq(0.01, 0.999, length.out = 401L), - 0.9999, 0.99999 -))) -method_colors <- c( - current = "grey45", `25%` = "#0072B2", `75%` = "#009E73", - `100%` = "#D55E00" -) - -dir.create(dirname(output_file), recursive = TRUE, showWarnings = FALSE) -pdf(output_file, width = 11, height = 7.5) -par(mfrow = c(2, 2), mar = c(4.3, 4.5, 2.3, 0.8), oma = c(0, 0, 3, 0)) -for (sample_size in sort(unique(results$sample_size))) { - current_results <- results[ - results$sample_size == sample_size & results$method == "current", - ] - fixed_results <- results[ - results$sample_size == sample_size & grepl("^fixed", results$method), - ] - fixed_results <- merge( - fixed_results, - current_results[, c("distribution", "global_ise", "boundary_ise")], - by = "distribution", suffixes = c("", "_current") - ) - for (metric in c("global", "boundary")) { - ratio_matrix <- vapply(fractions, function(fraction) { - selected_results <- fixed_results[ - fixed_results$method == paste0("fixed-", fraction, "pct"), - ] - selected_results[[paste0(metric, "_ise")]] / - selected_results[[paste0(metric, "_ise_current")]] - }, numeric(nrow(current_results))) - matplot( - fractions, t(ratio_matrix), type = "l", lty = 1, lwd = 1.4, - col = adjustcolor("grey40", 0.45), ylim = range(c(0.7, 1.1, ratio_matrix)), - xlab = "lowest sample fraction used for floor (%)", - ylab = "candidate / current ISE", - main = sprintf("%s ISE, n=%d", metric, sample_size) - ) - lines(fractions, colMeans(ratio_matrix), lwd = 3, col = "#009E73") - abline(h = 1, lty = 2) - } -} -mtext("Bandwidth-floor fraction: density-specific curves and mean", outer = TRUE, - font = 2, cex = 1.1) - -for (boundary_zoom in c(FALSE, TRUE)) { - par(mfrow = c(2, 3), mar = c(4.2, 4.2, 2.5, 0.5), oma = c(0, 0, 3, 0)) - for (sample_size in c(100L, 1000L)) { - for (distribution_index in seq_along(comparison_distributions)) { - evaluation_points <- comparison_distributions[[distribution_index]]$quantile( - evaluation_probabilities - ) - true_density <- comparison_distributions[[distribution_index]]$density( - evaluation_points - ) - set.seed( - 20260914L + 100000L * match( - names(comparison_distributions)[[distribution_index]], - c("exponential", "half_normal", "gamma_2", "gamma_0.75", "lomax_2") - ) + 1000L * match(sample_size, c(100L, 1000L)) + 1L - ) - observations <- comparison_distributions[[distribution_index]]$random( - sample_size - ) - estimates <- list( - current = normalize_one_sided_density( - evaluation_points, - dkde1d(evaluation_points, kde1d(observations, xmin = 0)) - ), - `25%` = fit_one_sided_candidate( - observations, evaluation_points, local_floor_fraction = 0.25 - )$density, - `75%` = fit_one_sided_candidate( - observations, evaluation_points, local_floor_fraction = 0.75 - )$density, - `100%` = fit_one_sided_candidate( - observations, evaluation_points, local_floor_fraction = 1 - )$density - ) - plotted_points <- if (boundary_zoom) { - evaluation_probabilities <= 0.2 - } else { - evaluation_probabilities <= 0.999 - } - plot( - evaluation_points[plotted_points], true_density[plotted_points], - type = "l", lwd = 3, col = "black", log = if (boundary_zoom) "x" else "", - ylim = c(0, quantile(c( - true_density[plotted_points], - unlist(lapply(estimates, function(density) density[plotted_points])) - ), 0.995)), - xlab = if (boundary_zoom) "distance from boundary" else "x", - ylab = "density", - main = sprintf( - "%s, n=%d", names(comparison_distributions)[[distribution_index]], - sample_size - ) - ) - for (method in names(estimates)) { - lines( - evaluation_points[plotted_points], estimates[[method]][plotted_points], - col = method_colors[[method]], lwd = if (method == "75%") 2.5 else 1.5, - lty = match(method, names(estimates)) - ) - } - if (sample_size == 100L && distribution_index == 1L) { - legend( - "topright", c("truth", names(estimates)), - col = c("black", method_colors), lty = c(1, seq_along(estimates)), - lwd = c(3, 1.5, 1.5, 2.5, 1.5), bty = "n", cex = 0.72 - ) - } - } - } - mtext( - if (boundary_zoom) "Representative boundary views" else - "Representative full-density views", - outer = TRUE, font = 2, cex = 1.1 - ) -} -dev.off() -message("wrote ", normalizePath(output_file)) diff --git a/diagnostic/plot_boundary_diagnostics.R b/diagnostic/plot_boundary_diagnostics.R deleted file mode 100644 index f7b4517..0000000 --- a/diagnostic/plot_boundary_diagnostics.R +++ /dev/null @@ -1,101 +0,0 @@ -args <- commandArgs(trailingOnly = TRUE) -if (length(args) != 1L) { - stop("usage: Rscript diagnostic/plot_boundary_diagnostics.R diagnostics.csv") -} - -results <- read.csv(args[[1]]) -results$pdf_ratio <- results$estimated_pdf / results$true_pdf -results$pdf_ratio[!is.finite(results$pdf_ratio) | results$pdf_ratio <= 0] <- - NA_real_ -results$cdf_error <- abs(results$estimated_cdf - results$true_cdf) - -tail_results <- subset(results, position <= 1e-2 & true_pdf > 0) -summary <- aggregate( - cbind(log_pdf_error = abs(log(pdf_ratio)), cdf_error = cdf_error) ~ - scenario + scale + degree + grid_size + bandwidth, - data = tail_results, - FUN = function(x) max(x, na.rm = TRUE) -) -summary <- summary[order(summary$log_pdf_error, summary$cdf_error), ] -cat("Worst tail errors\n") -print(head(summary[order(-summary$log_pdf_error), ], 20L), row.names = FALSE) - -results$scaled_pdf <- results$estimated_pdf * results$scale -scale_summary <- aggregate( - cbind(scaled_pdf = scaled_pdf, estimated_cdf = estimated_cdf) ~ - scenario + degree + grid_size + bandwidth + position, - data = subset(results, true_pdf > 0), - FUN = function(x) max(x) - min(x) -) -scale_summary$discrepancy <- pmax( - scale_summary$scaled_pdf, - scale_summary$estimated_cdf -) -cat("\nLargest scale-equivariance discrepancies\n") -print( - head(scale_summary[order(-scale_summary$discrepancy), ], 20L), - row.names = FALSE -) - -left <- subset(results, scenario == "exponential-left") -right <- subset(results, scenario == "exponential-right") -reflection <- merge( - left, - right, - by = c("scale", "degree", "grid_size", "bandwidth", "position"), - suffixes = c("_left", "_right") -) -reflection$pdf_error <- abs( - reflection$scaled_pdf_left - reflection$scaled_pdf_right -) -reflection$cdf_error <- abs( - reflection$estimated_cdf_left + reflection$estimated_cdf_right - 1 -) -cat("\nReflection-equivariance maxima\n") -cat("PDF:", max(reflection$pdf_error), "CDF:", max(reflection$cdf_error), "\n") - -grid_summary <- aggregate( - cbind(scaled_pdf = scaled_pdf, estimated_cdf = estimated_cdf) ~ - scenario + scale + degree + bandwidth + position, - data = subset(results, true_pdf > 0), - FUN = function(x) max(x) - min(x) -) -grid_summary$discrepancy <- pmax( - grid_summary$scaled_pdf, - grid_summary$estimated_cdf -) -cat("\nLargest grid-size discrepancies\n") -print( - head(grid_summary[order(-grid_summary$discrepancy), ], 20L), - row.names = FALSE -) - -pdf(sub("[.]csv$", ".pdf", args[[1]])) -for (scenario_name in unique(results$scenario)) { - selected <- subset( - results, - scenario == scenario_name & scale == 1 & grid_size == 400 & - bandwidth == "0.300000" & position > 0 & position <= 0.1 - ) - matplot( - selected$position[selected$degree == 0], - sapply(0:2, function(polynomial_degree) { - selected$estimated_pdf[selected$degree == polynomial_degree] - }), - type = "l", - log = "x", - lty = 1, - xlab = "distance from boundary / support scale", - ylab = "density", - main = scenario_name - ) - lines( - selected$position[selected$degree == 0], - selected$true_pdf[selected$degree == 0], - lty = 2, - lwd = 2 - ) - legend("topright", c("degree 0", "degree 1", "degree 2", "truth"), - col = c(1:3, 1), lty = c(1, 1, 1, 2), bty = "n") -} -dev.off() diff --git a/diagnostic/run_boundary_diagnostics.sh b/diagnostic/run_boundary_diagnostics.sh deleted file mode 100755 index a0ad5bb..0000000 --- a/diagnostic/run_boundary_diagnostics.sh +++ /dev/null @@ -1,20 +0,0 @@ -#!/bin/sh -set -eu - -diagnostic_source_dir=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd) -diagnostic_build_dir=${1:-"$diagnostic_source_dir/build-diagnostic"} - -cmake -S "$diagnostic_source_dir" -B "$diagnostic_build_dir" \ - -DCMAKE_BUILD_TYPE=Release \ - -DBUILD_TESTING=OFF \ - -DBUILD_DIAGNOSTICS=ON 1>&2 -cmake --build "$diagnostic_build_dir" \ - --target kde1d-boundary-diagnostic \ - --config Release 1>&2 - -diagnostic_executable="$diagnostic_build_dir/bin/kde1d-boundary-diagnostic" -if [ ! -x "$diagnostic_executable" ]; then - diagnostic_executable="$diagnostic_build_dir/bin/Release/kde1d-boundary-diagnostic.exe" -fi - -exec "$diagnostic_executable" diff --git a/diagnostic/validate_native_boundary_experts.R b/diagnostic/validate_native_boundary_experts.R index 2a0a79f..c552caf 100644 --- a/diagnostic/validate_native_boundary_experts.R +++ b/diagnostic/validate_native_boundary_experts.R @@ -1,5 +1,6 @@ -# Evaluate one native kde1d revision. Run once at the baseline commit and once -# at the candidate commit, then compare rows by scenario, size, and replication. +# Evaluate one native kde1d method. Install the pre-PR revision for `pre-pr`; +# install the candidate revision for `bulk` and `expert`. The pre-PR one-sided +# fit is the production log-transform estimator, not a local emulation of it. arguments <- commandArgs(trailingOnly = TRUE) if (length(arguments) < 2L || length(arguments) > 4L) { @@ -12,6 +13,9 @@ library(kde1d) method <- arguments[[1L]] output_file <- arguments[[2L]] +if (!method %in% c("pre-pr", "bulk", "expert")) { + stop("method must be one of: pre-pr, bulk, expert") +} replications <- if (length(arguments) >= 3L) { as.integer(arguments[[3L]]) } else { @@ -25,6 +29,14 @@ integrate_values <- function(points, values) { sum(diff(points) * (values[-length(values)] + values[-1L]) / 2) } +fit_kde1d <- function(observations, xmin = NA_real_, xmax = NA_real_) { + arguments <- list(x = observations, xmin = xmin, xmax = xmax) + if (method != "pre-pr") { + arguments$boundary_repair <- method == "expert" + } + do.call(kde1d, arguments) +} + one_sided <- list( exponential = list( random = function(n) rexp(n), @@ -62,6 +74,8 @@ two_sided <- list( beta_2_2 = c(2, 2) ) sample_sizes <- c(25L, 100L, 1000L, 2000L) +one_sided_scales <- c(1e-4, 1, 1e4) +one_sided_directions <- c("lower", "upper") result_rows <- list() summary_rows <- list() @@ -87,44 +101,69 @@ summarize_estimates <- function(points, estimates, truth, boundary) { for (scenario_index in seq_along(one_sided)) { scenario <- one_sided[[scenario_index]] - points <- sort(unique(c( + base_points <- sort(unique(c( 1e-10, scenario$quantile(10^seq(-8, -1, length.out = 100L)), scenario$quantile(seq(0.1, 0.9999, length.out = 401L)) ))) - truth <- scenario$density(points) - boundary <- points <= scenario$quantile(0.1) - for (sample_size in sample_sizes) { - estimates <- matrix(NA_real_, length(points), replications) - for (replication in seq_len(replications)) { - set.seed(20260824L + 100000L * scenario_index + - 1000L * match(sample_size, sample_sizes) + replication) - fit <- kde1d(scenario$random(sample_size), xmin = 0) - estimates[, replication] <- dkde1d(points, fit) - result_rows[[length(result_rows) + 1L]] <- data.frame( - support = "one-sided", - scenario = names(one_sided)[[scenario_index]], - sample_size = sample_size, - replication = replication, - method = method, - global_ise = integrate_values( - points, (estimates[, replication] - truth)^2 - ), - boundary_ise = integrate_values( - points[boundary], - (estimates[boundary, replication] - truth[boundary])^2 - ), - edf = fit$edf, - loglik = fit$loglik - ) + for (scale_index in seq_along(one_sided_scales)) { + scale <- one_sided_scales[[scale_index]] + scaled_points <- scale * base_points + scaled_truth <- scenario$density(base_points) / scale + for (direction_index in seq_along(one_sided_directions)) { + direction <- one_sided_directions[[direction_index]] + if (direction == "lower") { + points <- scaled_points + truth <- scaled_truth + boundary <- points <= scale * scenario$quantile(0.1) + } else { + points <- -rev(scaled_points) + truth <- rev(scaled_truth) + boundary <- points >= -scale * scenario$quantile(0.1) + } + for (sample_size in sample_sizes) { + estimates <- matrix(NA_real_, length(points), replications) + for (replication in seq_len(replications)) { + set.seed(20260824L + 10000000L * scenario_index + + 1000000L * scale_index + 100000L * direction_index + + 1000L * match(sample_size, sample_sizes) + replication) + observations <- scale * scenario$random(sample_size) + if (direction == "lower") { + fit <- fit_kde1d(observations, xmin = 0) + } else { + fit <- fit_kde1d(-observations, xmax = 0) + } + estimates[, replication] <- dkde1d(points, fit) + result_rows[[length(result_rows) + 1L]] <- data.frame( + support = "one-sided", + direction = direction, + scale = scale, + scenario = names(one_sided)[[scenario_index]], + sample_size = sample_size, + replication = replication, + method = method, + global_ise = integrate_values( + points, (estimates[, replication] - truth)^2 + ), + boundary_ise = integrate_values( + points[boundary], + (estimates[boundary, replication] - truth[boundary])^2 + ), + edf = fit$edf, + loglik = fit$loglik + ) + } + summary_rows[[length(summary_rows) + 1L]] <- data.frame( + support = "one-sided", + direction = direction, + scale = scale, + scenario = names(one_sided)[[scenario_index]], + sample_size = sample_size, + method = method, + as.list(summarize_estimates(points, estimates, truth, boundary)) + ) + } } - summary_rows[[length(summary_rows) + 1L]] <- data.frame( - support = "one-sided", - scenario = names(one_sided)[[scenario_index]], - sample_size = sample_size, - method = method, - as.list(summarize_estimates(points, estimates, truth, boundary)) - ) } } @@ -142,7 +181,7 @@ for (scenario_index in seq_along(two_sided)) { for (replication in seq_len(replications)) { set.seed(20260825L + 100000L * scenario_index + 1000L * match(sample_size, sample_sizes) + replication) - fit <- kde1d( + fit <- fit_kde1d( rbeta(sample_size, shapes[[1L]], shapes[[2L]]), xmin = 0, xmax = 1 @@ -150,6 +189,8 @@ for (scenario_index in seq_along(two_sided)) { estimates[, replication] <- dkde1d(points, fit) result_rows[[length(result_rows) + 1L]] <- data.frame( support = "two-sided", + direction = NA_character_, + scale = 1, scenario = names(two_sided)[[scenario_index]], sample_size = sample_size, replication = replication, @@ -167,6 +208,8 @@ for (scenario_index in seq_along(two_sided)) { } summary_rows[[length(summary_rows) + 1L]] <- data.frame( support = "two-sided", + direction = NA_character_, + scale = 1, scenario = names(two_sided)[[scenario_index]], sample_size = sample_size, method = method, diff --git a/docs/overview-continuous.dox b/docs/overview-continuous.dox index 28c1ed3..c3bd932 100644 --- a/docs/overview-continuous.dox +++ b/docs/overview-continuous.dox @@ -1,4 +1,113 @@ -/** @page overview-continuous Continuous Distributions +/** @page overview-continuous Continuous distributions +Continuous fits combine a transformed local-likelihood bulk estimator with an +optional finite-endpoint repair. The public `degree`, `bandwidth`, and +`multiplier` arguments retain their usual meaning for the bulk fit. Boundary +repair is enabled by default and can be disabled with `boundary_repair=false`. + +@section continuous-bulk Bulk estimator and support transforms + +With no finite support endpoint, data are fitted on their original scale. If +both endpoints @f$a power-3/4 transform + // left boundary -> regularized fourth-root transform x_new = 4.0 * (((boundary_offset_ + x.array() - xmin_) / boundary_scale_) .pow(0.25) - std::pow(boundary_offset_ / boundary_scale_, 0.25)); } else if (!std::isnan(xmax_)) { - // right boundary -> reflected power-3/4 transform + // right boundary -> reflected regularized fourth-root transform x_new = 4.0 * (((boundary_offset_ + xmax_ - x.array()) / boundary_scale_) .pow(0.25) - @@ -893,14 +900,14 @@ Kde1d::boundary_transform(const Eigen::VectorXd& x, bool inverse) auto rng = xmax_ - xmin_; x_new = stats::pnorm(x).array() * 1.0001 * rng + xmin_ - 5e-5 * rng; } else if (!std::isnan(xmin_)) { - // left boundary -> inverse power-3/4 transform + // left boundary -> inverse regularized fourth-root transform x_new = boundary_scale_ * (x.array() / 4.0 + std::pow(boundary_offset_ / boundary_scale_, 0.25)) .pow(4) + xmin_ - boundary_offset_; } else if (!std::isnan(xmax_)) { - // right boundary -> inverse reflected power-3/4 transform + // right boundary -> inverse reflected regularized fourth-root transform x_new = xmax_ + boundary_offset_ - boundary_scale_ * (x.array() / 4.0 + @@ -935,12 +942,12 @@ Kde1d::boundary_correct(const Eigen::VectorXd& x, const Eigen::VectorXd& fhat) corr_term /= (xmax_ - xmin_ + 1e-4 * rng); corr_term = 1.0 / corr_term.array(); } else if (!std::isnan(xmin_)) { - // left boundary -> power-3/4 transform + // left boundary -> fourth-root-transform Jacobian corr_term = ((boundary_offset_ + x.array() - xmin_) / boundary_scale_) .pow(-0.75) / boundary_scale_; } else if (!std::isnan(xmax_)) { - // right boundary -> reflected power-3/4 transform + // right boundary -> reflected fourth-root-transform Jacobian corr_term = ((boundary_offset_ + xmax_ - x.array()) / boundary_scale_) .pow(-0.75) / boundary_scale_; @@ -1420,8 +1427,7 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, // Bandwidth for Kernel Density Estimation //' @param x vector of observations //' @param bandwidth bandwidth parameter, NA for automatic selection. -//' @param multiplier bandwidth multiplieriplier. -//' @param discrete whether a jittered estimate is computed. +//' @param multiplier bandwidth multiplier. //' @param weights vector of weights for each observation (can be empty). //' @param degree polynomial degree. //' @return the selected bandwidth diff --git a/include/kde1d/kdefft.hpp b/include/kde1d/kdefft.hpp index 1434486..8485027 100644 --- a/include/kde1d/kdefft.hpp +++ b/include/kde1d/kdefft.hpp @@ -38,7 +38,7 @@ class KdeFFT //! @param bandwidth the bandwidth parameter. //! @param lower lower bound of the grid. //! @param upper bound of the grid. -//! @param weigths optional vector of weights for each observation. +//! @param weights optional vector of weights for each observation. //! @param num_bins number of bins for the FFT grid. inline KdeFFT::KdeFFT(const Eigen::VectorXd& x, double bandwidth, From 6d019672888a2d878e885166f70e6ed1581993a3 Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 21:04:27 +0200 Subject: [PATCH 18/25] Validate boundary repair for PR --- diagnostic/NATIVE_RESULTS.md | 52 ---- diagnostic/PR_COMMENT.md | 242 ++++++++++++++++++ diagnostic/README.md | 32 ++- .../benchmark_native_boundary_experts.R | 59 +++++ diagnostic/boundary-examples.png | Bin 0 -> 170831 bytes diagnostic/extract_native_boundary_examples.R | 116 +++++++++ diagnostic/plot_native_boundary_examples.R | 25 ++ .../summarize_native_boundary_validation.R | 228 +++++++++++++++++ diagnostic/validate_native_boundary_experts.R | 166 +++++++----- 9 files changed, 793 insertions(+), 127 deletions(-) delete mode 100644 diagnostic/NATIVE_RESULTS.md create mode 100644 diagnostic/PR_COMMENT.md create mode 100644 diagnostic/benchmark_native_boundary_experts.R create mode 100644 diagnostic/boundary-examples.png create mode 100644 diagnostic/extract_native_boundary_examples.R create mode 100644 diagnostic/plot_native_boundary_examples.R create mode 100644 diagnostic/summarize_native_boundary_validation.R diff --git a/diagnostic/NATIVE_RESULTS.md b/diagnostic/NATIVE_RESULTS.md deleted file mode 100644 index dcdfd56..0000000 --- a/diagnostic/NATIVE_RESULTS.md +++ /dev/null @@ -1,52 +0,0 @@ -# Native boundary-expert evidence - -The final comparison with the pre-PR estimator has not yet been run. Its -protocol is in [`README.md`](README.md). In particular, the one-sided primary -benchmark will be the actual production log-transform fit from pre-PR `main`, -not the unrepaired fourth-root fit used during development. - -The following implementation checks remain relevant to the selected method. - -## Selected implementation - -- Finite endpoints use the equal average of local-linear and local-quadratic - Gaussian equivalent kernels; the same expert is used for bulk degrees zero, - one, and two. -- Both kernels share an automatically selected degree-two bandwidth. Selection - uses all positive-weight observations on bounded support and the closest 75% - by row count on one-sided support. A manual bandwidth controls only the bulk; - the public multiplier scales both bandwidths. -- Public case weights are used by the classifier, expert estimand, expert - bandwidth selector, effective sample size, and influence approximation. -- A cubic CDF-based fusion region has probability width - $\min(0.25,n_e^{-1/2})$. Endpoints classified as exploding, vanishing, or - ambiguous retain the bulk fit. - -## FFT accuracy and runtime - -The endpoint kernels are pointwise combinations of an ordinary Gaussian KDE -and its first two derivatives, evaluated on a shared 256-bin FFT grid. In the -100-replication development suite, the mean relative ISE perturbation from FFT -binning was at most 0.011% in every support/sample-size group. Among active -experts, the median absolute paired ISE change was 0.023%, the 99th percentile -was 0.18%, and the maximum was 0.66%. - -The direct-kernel fallback was rejected. Across 51--401 output grid points at -$n=25,100$, always using FFT slowed the worst case by 1.25x. On the default -grid at $n=100$, one active endpoint changed from 0.64 to 0.67 ms and two -active endpoints from 0.77 to 0.74 ms. At $n=2000$, FFT reduced one-endpoint -fit time from 1.21 to 0.92 ms and two-endpoint time from 2.25 to 0.96 ms. - -## EDF approximation - -The conditional mixture EDF was checked against - -$$ -1+\sum_i\{\log\widehat f(X_i)-\log\widehat f_{-i}(X_i)\}. -$$ - -For deterministic finite-endpoint samples at $n=25,50,100$, discrepancies -were 0.08--0.30 EDF units for Uniform and Exponential examples. For -Beta$(1,2)$ they were 0.27--0.33 at $n=50,100$ and 0.84 at $n=25$. This was -considered adequate for an asymptotic trace approximation that already holds -bandwidths fixed. Pure-bulk fits retain the prior EDF calculation exactly. diff --git a/diagnostic/PR_COMMENT.md b/diagnostic/PR_COMMENT.md new file mode 100644 index 0000000..9ee0435 --- /dev/null +++ b/diagnostic/PR_COMMENT.md @@ -0,0 +1,242 @@ +## Boundary-repair estimator + +This PR changes continuous fits with known finite support in two steps. + +For a one-sided support, write $d(x)$ for distance from the finite endpoint, +let $s$ be the weighted median observed distance, and set +$\epsilon=10^{-5}s$. The transformed bulk estimator now uses + +$$ +T\{d(x)\} +=4\left[\left\{\frac{d(x)+\epsilon}{s}\right\}^{1/4} +-\left(\frac{\epsilon}{s}\right)^{1/4}\right], +\qquad +|T'(x)| +=\frac{1}{s}\left\{\frac{d(x)+\epsilon}{s}\right\}^{-3/4}. +$$ + +This replaces the previous log transform and makes the construction scale +equivariant. Two-sided fits retain the regularized probit bulk transform. + +Each finite endpoint is then classified independently from its first +$k\simeq2\sqrt{n_e}$ order statistics. In the unweighted case, + +$$ +\widehat\beta +=\frac{k}{\sum_{i=1}^k +\log\{d_{(k+1)}/d_{(i)}\}}. +$$ + +Endpoints consistent with a finite nonzero limiting density receive a boundary +expert. Exploding, vanishing, ambiguous, and degenerate endpoints retain the +bulk. The expert is the equal average + +$$ +\widehat f_E=(\widehat f_{\mathrm{local\ linear}} + +\widehat f_{\mathrm{local\ quadratic}})/2 +$$ + +of Gaussian equivalent-kernel estimates. Both kernels share an automatically +selected degree-2 plug-in bandwidth on the original scale, using all +positive-weight observations on bounded support and the closest 75% by row +count on one-sided support. The three required Gaussian convolutions are +evaluated on a shared 256-bin FFT grid. + +Let $F_B$ be the normalized bulk CDF, + +$$ +q=\min(1/4,n_e^{-1/2}), +\qquad +g(p)=1-3\min(1,p/q)^2+2\min(1,p/q)^3. +$$ + +Selected lower and upper experts receive weights +$w_L(x)=g\{F_B(x)\}$ and $w_U(x)=g\{1-F_B(x)\}$, giving + +$$ +\widehat f(x) +=w_L(x)\widehat f_L(x) ++\{1-w_L(x)-w_U(x)\}\widehat f_B(x) ++w_U(x)\widehat f_U(x). +$$ + +The result is clamped at zero and normalized. The same boundary expert is used +for bulk degrees 0, 1, and 2. EDF is a conditional influence-trace +approximation that holds the classifier, selected bandwidths, fusion weights, +clamps, and normalization fixed. + +## Validation design + +The primary benchmark is the actual pre-PR package at parent commit `7faec53` +with C++ commit `b16d514`: log transform for one-sided support and probit for +two-sided support. The experiment used 200 paired replications for +$n\in\{25,100,1000,2000\}$ and degrees 0, 1, and 2. + +- One-sided: Exponential, half-normal, Gamma$(0.75)$, Gamma$(2)$, and + Lomax$(2)$, with lower/upper reflections and scales $10^{-4},1,10^4$. +- Two-sided: Uniform and Beta$(1,2)$, Beta$(2,1)$, Beta$(0.75,2)$, + Beta$(2,0.75)$, Beta$(0.75,0.75)$, and Beta$(2,2)$. +- Global ISE and boundary ISE were integrated separately. The boundary region + is the outer 10% probability mass at each finite endpoint. + +The tables below use scale 1; reflected one-sided results agree to numerical +precision. Entries are candidate/baseline ratios, so **values below 1 favor the +PR**. Parentheses are paired Monte Carlo standard errors. + +### Global ISE ratio, averaged over families + +| support | degree | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:|---:| +| one-sided | 0 | 0.748 (0.044) | 0.579 (0.028) | 0.513 (0.011) | 0.475 (0.010) | +| one-sided | 1 | 0.505 (0.020) | 0.411 (0.011) | 0.684 (0.063) | 0.724 (0.050) | +| one-sided | 2 | 0.211 (0.036) | 0.198 (0.021) | 0.208 (0.018) | 0.260 (0.015) | +| two-sided | 0 | 0.951 (0.005) | 0.943 (0.005) | 0.941 (0.006) | 0.925 (0.005) | +| two-sided | 1 | 0.867 (0.006) | 0.823 (0.007) | 0.847 (0.005) | 0.852 (0.004) | +| two-sided | 2 | 0.892 (0.013) | 0.911 (0.006) | 0.940 (0.006) | 0.932 (0.006) | + +### Boundary ratio, averaged over families + +| support | degree | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:|---:| +| one-sided | 0 | 0.702 (0.049) | 0.513 (0.030) | 0.447 (0.013) | 0.399 (0.011) | +| one-sided | 1 | 0.399 (0.022) | 0.303 (0.011) | 0.636 (0.075) | 0.702 (0.059) | +| one-sided | 2 | 0.144 (0.027) | 0.151 (0.027) | 0.159 (0.016) | 0.205 (0.015) | +| two-sided | 0 | 0.923 (0.005) | 0.944 (0.005) | 0.954 (0.005) | 0.939 (0.005) | +| two-sided | 1 | 0.824 (0.008) | 0.826 (0.007) | 0.879 (0.004) | 0.877 (0.004) | +| two-sided | 2 | 0.883 (0.012) | 0.913 (0.005) | 0.955 (0.005) | 0.945 (0.005) | + +The expert also improves over the unrepaired new bulk. Averaged global ISE +ratios range from 0.84--0.94 for degree 0, 0.74--0.89 for degree 1, and +0.88--0.92 for degree 2 on one-sided support. The corresponding bounded ratios +are 0.93--0.95, 0.82--0.87, and 0.89--0.94. + +
+Family-level global / boundary ISE ratios + +#### One-sided, degree 0 + +| family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:| +| Exponential | 0.75 / 0.73 | 0.49 / 0.45 | 0.37 / 0.30 | 0.34 / 0.27 | +| Gamma$(0.75)$ | 0.55 / 0.54 | 0.51 / 0.50 | 0.45 / 0.44 | 0.44 / 0.43 | +| Gamma$(2)$ | 0.71 / 0.52 | 0.76 / 0.58 | 0.81 / 0.69 | 0.80 / 0.67 | +| half-normal | 0.46 / 0.38 | 0.41 / 0.32 | 0.31 / 0.21 | 0.28 / 0.17 | +| Lomax$(2)$ | 1.28 / 1.34 | 0.72 / 0.70 | 0.63 / 0.59 | 0.51 / 0.45 | + +#### One-sided, degree 1 + +| family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:| +| Exponential | 0.49 / 0.37 | 0.31 / 0.22 | 0.38 / 0.26 | 0.38 / 0.27 | +| Gamma$(0.75)$ | 0.27 / 0.25 | 0.25 / 0.21 | 0.45 / 0.43 | 0.53 / 0.52 | +| Gamma$(2)$ | 0.69 / 0.46 | 0.81 / 0.63 | 0.93 / 0.98 | 1.01 / 1.19 | +| half-normal | 0.45 / 0.32 | 0.38 / 0.23 | 0.43 / 0.25 | 0.43 / 0.25 | +| Lomax$(2)$ | 0.62 / 0.60 | 0.31 / 0.22 | 1.23 / 1.26 | 1.27 / 1.28 | + +#### One-sided, degree 2 + +| family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:| +| Exponential | 0.07 / 0.04 | 0.02 / 0.01 | 0.06 / 0.04 | 0.09 / 0.06 | +| Gamma$(0.75)$ | 0.03 / 0.03 | 0.04 / 0.03 | 0.23 / 0.21 | 0.23 / 0.21 | +| Gamma$(2)$ | 0.38 / 0.18 | 0.72 / 0.56 | 0.59 / 0.44 | 0.62 / 0.50 | +| half-normal | 0.09 / 0.04 | 0.03 / 0.02 | 0.03 / 0.01 | 0.06 / 0.03 | +| Lomax$(2)$ | 0.49 / 0.43 | 0.17 / 0.13 | 0.13 / 0.09 | 0.30 / 0.23 | + +#### Two-sided, degree 0 + +| family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:| +| Beta$(0.75,0.75)$ | 1.02 / 1.03 | 1.03 / 1.04 | 1.04 / 1.04 | 1.05 / 1.05 | +| Beta$(0.75,2)$ | 0.99 / 0.98 | 1.01 / 1.00 | 1.07 / 1.07 | 1.06 / 1.06 | +| Beta$(1,2)$ | 0.93 / 0.91 | 0.85 / 0.86 | 0.83 / 0.86 | 0.78 / 0.81 | +| Beta$(2,0.75)$ | 1.00 / 0.99 | 1.01 / 1.00 | 1.09 / 1.08 | 1.06 / 1.05 | +| Beta$(2,1)$ | 0.95 / 0.93 | 0.89 / 0.89 | 0.78 / 0.81 | 0.79 / 0.82 | +| Beta$(2,2)$ | 0.82 / 0.65 | 0.94 / 0.88 | 1.00 / 1.00 | 1.00 / 1.00 | +| Uniform | 0.95 / 0.98 | 0.88 / 0.93 | 0.77 / 0.82 | 0.74 / 0.79 | + +#### Two-sided, degree 1 + +| family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:| +| Beta$(0.75,0.75)$ | 0.91 / 0.91 | 0.87 / 0.88 | 0.94 / 0.95 | 0.97 / 0.97 | +| Beta$(0.75,2)$ | 0.88 / 0.87 | 0.89 / 0.90 | 0.96 / 0.97 | 0.98 / 0.98 | +| Beta$(1,2)$ | 0.81 / 0.76 | 0.72 / 0.74 | 0.73 / 0.76 | 0.69 / 0.73 | +| Beta$(2,0.75)$ | 0.89 / 0.88 | 0.88 / 0.88 | 0.95 / 0.96 | 0.98 / 0.98 | +| Beta$(2,1)$ | 0.86 / 0.82 | 0.74 / 0.76 | 0.70 / 0.75 | 0.71 / 0.74 | +| Beta$(2,2)$ | 0.91 / 0.73 | 0.96 / 0.90 | 1.00 / 1.00 | 1.00 / 1.00 | +| Uniform | 0.82 / 0.78 | 0.70 / 0.72 | 0.64 / 0.77 | 0.62 / 0.74 | + +#### Two-sided, degree 2 + +| family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | +|---|---:|---:|---:|---:| +| Beta$(0.75,0.75)$ | 0.91 / 0.92 | 0.95 / 0.96 | 1.02 / 1.02 | 1.05 / 1.05 | +| Beta$(0.75,2)$ | 0.89 / 0.89 | 0.94 / 0.94 | 1.06 / 1.06 | 1.06 / 1.05 | +| Beta$(1,2)$ | 0.77 / 0.80 | 0.84 / 0.85 | 0.82 / 0.85 | 0.78 / 0.81 | +| Beta$(2,0.75)$ | 0.90 / 0.90 | 0.94 / 0.95 | 1.08 / 1.07 | 1.05 / 1.05 | +| Beta$(2,1)$ | 0.90 / 0.90 | 0.83 / 0.85 | 0.78 / 0.82 | 0.79 / 0.83 | +| Beta$(2,2)$ | 0.99 / 0.89 | 1.02 / 0.95 | 1.00 / 1.00 | 1.00 / 1.00 | +| Uniform | 0.87 / 0.87 | 0.86 / 0.90 | 0.82 / 0.86 | 0.79 / 0.83 | + +
+ +## Bias, variance, classification, and scale + +The ISE gains are primarily a variance reduction, with some deliberate +small-sample boundary bias. Against pre-PR at scale 1, aggregate global +variance ratios are 0.27--0.53 one-sided for degree 0, 0.29--0.43 for degree 1, +and 0.04--0.12 for degree 2. Bounded ratios are 0.99--1.03, 0.86--0.90, and +0.89--1.00, respectively. This matches the visual goal: substantially calmer +one-sided endpoints and moderate smoothing on bounded support. + +Classifier behavior becomes appropriately conservative with sample size. For +one-sided finite targets, selection rates at $n=100/2000$ are 58%/78% +(Exponential), 75%/82% (half-normal), and 56%/76% (Lomax). False finite +selection falls from 22% to 4% for Gamma$(0.75)$ and from 38% to 0% for +Gamma$(2)$. For Uniform, either endpoint is selected in 90%/98% and both in +51%/71% of samples. Beta$(2,2)$ falls from 4.5% both-endpoint selection at +$n=100$ to 0% at $n\geq1000$. + +For Exponential samples at $n=100$, the 5%--95% range of the estimated value +at the endpoint is 0.56--1.44 when the expert is selected, compared with +0.01--49.6 when the classifier retains the raw bulk. Thus the expert delivers +the intended visual stabilization when selected; remaining extreme endpoint +values are primarily classifier false negatives. + + + + +## Coarse runtime + +Median end-to-end R fit times for the default degree-2 estimator are below. + +| case | $n$ | pre-PR | candidate | slowdown | +|---|---:|---:|---:|---:| +| one active endpoint | 100 | 0.48 ms | 0.81 ms | 1.70x | +| one active endpoint | 1,000 | 1.51 ms | 1.96 ms | 1.29x | +| one active endpoint | 10,000 | 12.43 ms | 13.57 ms | 1.09x | +| two active endpoints | 100 | 0.51 ms | 0.87 ms | 1.71x | +| two active endpoints | 1,000 | 1.45 ms | 1.85 ms | 1.27x | +| two active endpoints | 10,000 | 10.97 ms | 11.83 ms | 1.08x | +| one-sided fallback | 100 / 1,000 / 10,000 | -- | -- | 1.09x / 1.05x / 1.02x | +| two-sided fallback | 100 / 1,000 / 10,000 | -- | -- | 1.00x / 1.01x / 1.01x | + +## Less common paths and numerical checks + +- Public case weights are used consistently by the classifier, expert + estimand, bandwidth selector, effective sample size, and EDF approximation. + Tests cover weight rescaling and zero-weight-row invariance. +- A manually supplied bandwidth controls the transformed bulk only. Boundary + experts retain their original-scale automatic bandwidth; the public + multiplier scales both. This unusual path has focused regression tests but + was not included in the full Monte Carlo sweep. +- Setting `boundary_repair=false` recovers the transformed bulk and skips all + expert work. +- Tests cover degrees 0--2, normalization, nonnegativity, monotone CDFs, + quantile round trips, support truncation, reflection, scales $10^{-4}$ to + $10^4$, weights, fixed bandwidths, and pure-bulk EDF parity. +- The conditional EDF approximation differed from leave-one-out optimism by + about 0.08--0.30 EDF units for deterministic Uniform/Exponential examples; + the largest checked discrepancy was 0.84 for Beta$(1,2)$ at $n=25$. diff --git a/diagnostic/README.md b/diagnostic/README.md index b3d7eec..2d73909 100644 --- a/diagnostic/README.md +++ b/diagnostic/README.md @@ -12,7 +12,7 @@ a time. Run it with these method labels: | method | installed revision | estimator | |---|---|---| -| `pre-pr` | pre-PR `main` (`1260b5e` for the planned comparison) | production log transform on one-sided support and probit transform on two-sided support | +| `pre-pr` | parent `7faec53`, with C++ `b16d514` | production log transform on one-sided support and probit transform on two-sided support | | `bulk` | candidate | fourth-root/probit bulk with `boundary_repair = FALSE` | | `expert` | candidate | fourth-root/probit bulk with the selected boundary experts | @@ -22,9 +22,10 @@ benchmark. The suite covers lower- and upper-bounded versions of five one-sided densities at scales `1e-4`, `1`, and `1e4`, seven two-sided densities, and sample sizes -25, 100, 1,000, and 2,000. It writes replication-level global and boundary ISE, -EDF, and log-likelihood, plus integrated squared bias and variance summaries. -Paired seeds are shared across methods. +25, 100, 1,000, and 2,000 for bulk degrees zero, one, and two. It writes +replication-level global and boundary ISE, EDF, and log-likelihood, plus +integrated squared bias and variance summaries. Paired seeds are shared across +methods and degrees. From the R-package root, install each requested revision into a separate library and run, for example: @@ -39,10 +40,21 @@ Rscript inst/include/kde1d-cpp/diagnostic/validate_native_boundary_experts.R \ ``` Generated CSVs and figures are not versioned. The final aggregate comparison -and representative plots should be recorded in `NATIVE_RESULTS.md` after the -validation is complete. +is generated with: -`NATIVE_RESULTS.md` currently retains only implementation-level evidence that -still applies to the selected estimator. Superseded R prototypes, candidate -estimators, tuning outputs, and the standalone C++ diagnostic were removed; -stable numerical properties are covered by the unit and invariant tests. +```sh +Rscript inst/include/kde1d-cpp/diagnostic/summarize_native_boundary_validation.R \ + diagnostic-results/pre-pr.csv diagnostic-results/bulk.csv \ + diagnostic-results/expert.csv diagnostic-results/ratios +``` + +`benchmark_native_boundary_experts.R` performs coarse end-to-end R timings. +`extract_native_boundary_examples.R` and +`plot_native_boundary_examples.R` recreate the representative density montage +using classifier-stratified median-ISE realizations selected by the summary +script. + +Final results are recorded in `NATIVE_RESULTS.md`; `PR_COMMENT.md` contains the +copy-ready methodological description and report. Superseded R prototypes, +candidate estimators, tuning outputs, and the standalone C++ diagnostic were +removed; stable numerical properties are covered by unit and invariant tests. diff --git a/diagnostic/benchmark_native_boundary_experts.R b/diagnostic/benchmark_native_boundary_experts.R new file mode 100644 index 0000000..6458303 --- /dev/null +++ b/diagnostic/benchmark_native_boundary_experts.R @@ -0,0 +1,59 @@ +arguments <- commandArgs(trailingOnly = TRUE) +if (length(arguments) != 3L) { + stop("usage: script method output.csv library-path") +} +.libPaths(c(arguments[[3L]], .libPaths())) +library(kde1d) + +method <- arguments[[1L]] +if (!method %in% c("pre-pr", "bulk", "expert")) { + stop("method must be one of: pre-pr, bulk, expert") +} + +fit_kde1d <- function(observations, xmin, xmax) { + fit_arguments <- list(x = observations, xmin = xmin, xmax = xmax, deg = 2) + if (method != "pre-pr") { + fit_arguments$boundary_repair <- method == "expert" + } + do.call(kde1d, fit_arguments) +} + +make_observations <- function(case, n) { + probabilities <- seq(0.5 / n, 1 - 0.5 / n, length.out = n) + switch( + case, + one_active = -log1p(-probabilities), + one_fallback = sqrt(probabilities), + two_active = probabilities, + two_fallback = qbeta(probabilities, 2, 2) + ) +} + +rows <- list() +for (case in c("one_active", "one_fallback", "two_active", "two_fallback")) { + for (n in c(100L, 1000L, 10000L)) { + observations <- make_observations(case, n) + one_sided <- startsWith(case, "one_") + xmin <- 0 + xmax <- if (one_sided) NaN else 1 + iterations <- if (n == 100L) 500L else if (n == 1000L) 200L else 30L + fit_kde1d(observations, xmin, xmax) + for (batch in seq_len(7L)) { + elapsed <- system.time({ + for (iteration in seq_len(iterations)) { + fit_kde1d(observations, xmin, xmax) + } + })[["elapsed"]] + rows[[length(rows) + 1L]] <- data.frame( + method = method, + case = case, + sample_size = n, + batch = batch, + milliseconds = 1000 * elapsed / iterations + ) + } + } +} + 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z1ONgCMGgk$=1ESQ9u{mS86H1Hy2><*B=H5**f02UJqxCa7m#KSNbh&SR#Vwsss&PpVh9Mm{wh%f#dX#Iab b!~DbU{%7#PPdR%E;>lGMH0879OoRRd8;meo literal 0 HcmV?d00001 diff --git a/diagnostic/extract_native_boundary_examples.R b/diagnostic/extract_native_boundary_examples.R new file mode 100644 index 0000000..07ce3b1 --- /dev/null +++ b/diagnostic/extract_native_boundary_examples.R @@ -0,0 +1,116 @@ +arguments <- commandArgs(trailingOnly = TRUE) +if (length(arguments) != 4L) { + stop("usage: script method output.csv library-path selections.csv") +} +.libPaths(c(arguments[[3L]], .libPaths())) +library(kde1d) + +method <- arguments[[1L]] +if (!method %in% c("pre-pr", "bulk", "expert")) { + stop("method must be one of: pre-pr, bulk, expert") +} + +fit_kde1d <- function(observations, xmin, xmax) { + fit_arguments <- list(x = observations, xmin = xmin, xmax = xmax, deg = 2) + if (method != "pre-pr") { + fit_arguments$boundary_repair <- method == "expert" + } + do.call(kde1d, fit_arguments) +} + +one_sided <- list( + exponential = list(random = rexp, density = dexp, quantile = qexp), + half_normal = list( + random = function(n) abs(rnorm(n)), + density = function(x) 2 * dnorm(x), + quantile = function(p) qnorm((p + 1) / 2) + ), + gamma_075 = list( + random = function(n) rgamma(n, 0.75), + density = function(x) dgamma(x, 0.75), + quantile = function(p) qgamma(p, 0.75) + ), + gamma_2 = list( + random = function(n) rgamma(n, 2), + density = function(x) dgamma(x, 2), + quantile = function(p) qgamma(p, 2) + ) +) +two_sided <- list( + uniform = list(shape1 = 1, shape2 = 1), + beta_1_2 = list(shape1 = 1, shape2 = 2), + beta_075_2 = list(shape1 = 0.75, shape2 = 2), + beta_2_2 = list(shape1 = 2, shape2 = 2) +) +selections <- read.csv(arguments[[4L]], stringsAsFactors = FALSE) + +rows <- list() +for (scenario_index in seq_along(one_sided)) { + scenario <- one_sided[[scenario_index]] + selection <- selections[ + selections$support == "one-sided" & + selections$scenario == names(one_sided)[[scenario_index]], + ] + sample_size_index <- match(selection$sample_size, c(25L, 100L, 1000L, 2000L)) + set.seed(20260824L + 10000000L * scenario_index + + 1000L * sample_size_index + selection$replication) + observations <- scenario$random(selection$sample_size) + points <- sort(unique(c( + 1e-10, + scenario$quantile(10^seq(-8, -1, length.out = 120L)), + scenario$quantile(seq(0.1, 0.999, length.out = 300L)) + ))) + if (is.finite(scenario$density(0))) { + points <- c(0, points) + } + fit <- fit_kde1d(observations, 0, NaN) + rows[[length(rows) + 1L]] <- data.frame( + method = method, + support = "one-sided", + scenario = paste0( + names(one_sided)[[scenario_index]], "_n", selection$sample_size + ), + sample_size = selection$sample_size, + x = points, + truth = scenario$density(points), + estimate = dkde1d(points, fit) + ) +} + +points <- sort(unique(c( + 10^seq(-10, -2, length.out = 121L), + seq(0.01, 0.99, length.out = 301L), + 1 - 10^seq(-2, -10, length.out = 121L) +))) +for (scenario_index in seq_along(two_sided)) { + scenario <- two_sided[[scenario_index]] + selection <- selections[ + selections$support == "two-sided" & + selections$scenario == names(two_sided)[[scenario_index]], + ] + sample_size_index <- match(selection$sample_size, c(25L, 100L, 1000L, 2000L)) + set.seed(20260825L + 100000L * scenario_index + + 1000L * sample_size_index + selection$replication) + observations <- rbeta( + selection$sample_size, scenario$shape1, scenario$shape2 + ) + scenario_points <- points + if (scenario$shape1 >= 1 && scenario$shape2 >= 1) { + scenario_points <- c(0, points, 1) + } + fit <- fit_kde1d(observations, 0, 1) + rows[[length(rows) + 1L]] <- data.frame( + method = method, + support = "two-sided", + scenario = paste0( + names(two_sided)[[scenario_index]], "_n", selection$sample_size + ), + sample_size = selection$sample_size, + x = scenario_points, + truth = dbeta(scenario_points, scenario$shape1, scenario$shape2), + estimate = dkde1d(scenario_points, fit) + ) +} + +dir.create(dirname(arguments[[2L]]), recursive = TRUE, showWarnings = FALSE) +write.csv(do.call(rbind, rows), arguments[[2L]], row.names = FALSE) diff --git a/diagnostic/plot_native_boundary_examples.R b/diagnostic/plot_native_boundary_examples.R new file mode 100644 index 0000000..25b8182 --- /dev/null +++ b/diagnostic/plot_native_boundary_examples.R @@ -0,0 +1,25 @@ +arguments <- commandArgs(trailingOnly = TRUE) +if (length(arguments) != 4L) { + stop("usage: script pre-pr.csv bulk.csv expert.csv output.png") +} +library(ggplot2) + +estimates <- do.call(rbind, lapply(arguments[1:3], read.csv)) +estimates$method <- factor( + estimates$method, + levels = c("pre-pr", "bulk", "expert"), + labels = c("pre-PR log/probit", "new bulk", "new bulk + experts") +) +truth <- unique(estimates[c("support", "scenario", "sample_size", "x", "truth")]) + +plot <- ggplot(estimates, aes(x, estimate, color = method)) + + geom_line(linewidth = 0.55) + + geom_line(data = truth, aes(x = x, y = truth), inherit.aes = FALSE, + color = "black", linewidth = 0.65, linetype = 2) + + facet_wrap(~scenario, scales = "free", ncol = 2) + + scale_color_manual(values = c("#777777", "#377eb8", "#e41a1c")) + + labs(x = NULL, y = "density", color = NULL) + + theme_bw(base_size = 9) + + theme(legend.position = "bottom") + +ggsave(arguments[[4L]], plot, width = 8, height = 10, dpi = 160) diff --git a/diagnostic/summarize_native_boundary_validation.R b/diagnostic/summarize_native_boundary_validation.R new file mode 100644 index 0000000..ba24502 --- /dev/null +++ b/diagnostic/summarize_native_boundary_validation.R @@ -0,0 +1,228 @@ +arguments <- commandArgs(trailingOnly = TRUE) +if (length(arguments) != 4L) { + stop("usage: script pre-pr.csv bulk.csv expert.csv output-prefix") +} + +read_results <- function(path) { + results <- read.csv(path, stringsAsFactors = FALSE) + results$direction[is.na(results$direction)] <- "none" + results +} + +pre_pr <- read_results(arguments[[1L]]) +bulk <- read_results(arguments[[2L]]) +expert <- read_results(arguments[[3L]]) +output_prefix <- arguments[[4L]] +keys <- c( + "support", "direction", "scale", "scenario", "degree", "sample_size", + "replication" +) + +paired_ratios <- function(reference, comparison) { + paired <- merge( + expert, + reference, + by = keys, + suffixes = c("_expert", "_reference") + ) + groups <- split( + seq_len(nrow(paired)), + interaction(paired[c( + "support", "direction", "scale", "scenario", "degree", "sample_size" + )], drop = TRUE) + ) + rows <- lapply(groups, function(index) { + lapply(c("global_ise", "boundary_ise"), function(metric) { + candidate <- paired[[paste0(metric, "_expert")]][index] + baseline <- paired[[paste0(metric, "_reference")]][index] + ratio <- mean(candidate) / mean(baseline) + data.frame( + comparison = comparison, + metric = metric, + paired[index[[1L]], c( + "support", "direction", "scale", "scenario", "degree", + "sample_size" + )], + ratio = ratio, + mcse = sd(candidate - ratio * baseline) / + (sqrt(length(index)) * mean(baseline)) + ) + }) + }) + do.call(rbind, unlist(rows, recursive = FALSE)) +} + +cell_ratios <- rbind( + paired_ratios(pre_pr, "pre-pr"), + paired_ratios(bulk, "bulk") +) + +# Average scale/reflection cells within a family while retaining their paired +# covariance. Different families use independent simulation streams. +family_paired_ratios <- function(reference, comparison) { + paired <- merge( + expert, + reference, + by = keys, + suffixes = c("_expert", "_reference") + ) + cell_names <- c( + "support", "direction", "scale", "scenario", "degree", "sample_size" + ) + family_names <- c("support", "scenario", "degree", "sample_size") + rows <- lapply(c("global_ise", "boundary_ise"), function(metric) { + paired$cell <- interaction(paired[cell_names], drop = TRUE) + paired$influence <- NA_real_ + paired$cell_ratio <- NA_real_ + for (index in split(seq_len(nrow(paired)), paired$cell)) { + candidate <- paired[[paste0(metric, "_expert")]][index] + baseline <- paired[[paste0(metric, "_reference")]][index] + ratio <- mean(candidate) / mean(baseline) + paired$cell_ratio[index] <- ratio + paired$influence[index] <- + (candidate - ratio * baseline) / mean(baseline) + } + family_groups <- split( + seq_len(nrow(paired)), interaction(paired[family_names], drop = TRUE) + ) + lapply(family_groups, function(index) { + first_cell_rows <- index[!duplicated(paired$cell[index])] + replication_groups <- split(index, paired$replication[index]) + replication_influence <- vapply( + replication_groups, + function(replication_index) mean(paired$influence[replication_index]), + numeric(1) + ) + data.frame( + comparison = comparison, + metric = metric, + paired[index[[1L]], family_names, drop = FALSE], + ratio = mean(paired$cell_ratio[first_cell_rows]), + mcse = sd(replication_influence) / sqrt(length(replication_influence)), + cells = length(first_cell_rows) + ) + }) + }) + do.call(rbind, unlist(rows, recursive = FALSE)) +} + +family_ratios <- rbind( + family_paired_ratios(pre_pr, "pre-pr"), + family_paired_ratios(bulk, "bulk") +) +support_names <- c( + "comparison", "metric", "support", "degree", "sample_size" +) +support_groups <- split( + seq_len(nrow(family_ratios)), + interaction(family_ratios[support_names], drop = TRUE) +) +support_ratios <- do.call(rbind, lapply(support_groups, function(index) { + data.frame( + family_ratios[index[[1L]], support_names, drop = FALSE], + ratio = mean(family_ratios$ratio[index]), + mcse = sqrt(sum(family_ratios$mcse[index]^2)) / length(index), + cells = sum(family_ratios$cells[index]) + ) +})) + +classification <- expert[ + expert$degree == 0 & + ((expert$support == "one-sided" & expert$scale == 1 & + expert$direction == "lower") | expert$support == "two-sided"), +] +activation_groups <- split( + seq_len(nrow(classification)), + interaction(classification[c("support", "scenario", "sample_size")], + drop = TRUE) +) +activation <- do.call(rbind, lapply(activation_groups, function(index) { + data.frame( + classification[index[[1L]], c("support", "scenario", "sample_size")], + lower_rate = mean(classification$repair_lower[index]), + upper_rate = mean(classification$repair_upper[index]), + any_rate = mean( + classification$repair_lower[index] | classification$repair_upper[index] + ), + both_rate = mean( + classification$repair_lower[index] & classification$repair_upper[index] + ) + ) +})) + +read_summaries <- function(path) { + summary <- read.csv(path, stringsAsFactors = FALSE) + summary$direction[is.na(summary$direction)] <- "none" + summary +} +summary_path <- function(path) sub("\\.csv$", "-summary.csv", path) +pre_pr_summary <- read_summaries(summary_path(arguments[[1L]])) +bulk_summary <- read_summaries(summary_path(arguments[[2L]])) +expert_summary <- read_summaries(summary_path(arguments[[3L]])) +summary_keys <- keys[keys != "replication"] + +component_ratios <- function(reference, comparison) { + paired <- merge( + expert_summary, + reference, + by = summary_keys, + suffixes = c("_expert", "_reference") + ) + metrics <- c( + "global_squared_bias", "global_variance", + "boundary_squared_bias", "boundary_variance" + ) + do.call(rbind, lapply(metrics, function(metric) { + data.frame( + comparison = comparison, + metric = metric, + paired[summary_keys], + ratio = paired[[paste0(metric, "_expert")]] / + paired[[paste0(metric, "_reference")]] + ) + })) +} + +components <- rbind( + component_ratios(pre_pr_summary, "pre-pr"), + component_ratios(bulk_summary, "bulk") +) + +example_targets <- data.frame( + support = c(rep("one-sided", 4), rep("two-sided", 4)), + scenario = c( + "exponential", "half_normal", "gamma_075", "gamma_2", + "uniform", "beta_1_2", "beta_075_2", "beta_2_2" + ), + sample_size = c(100L, 25L, 1000L, 1000L, 100L, 1000L, 1000L, 1000L), + repair_lower = c(TRUE, TRUE, FALSE, FALSE, TRUE, TRUE, FALSE, FALSE), + repair_upper = c(FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE) +) +example_rows <- lapply(seq_len(nrow(example_targets)), function(i) { + target <- example_targets[i, ] + candidates <- expert[ + expert$support == target$support & + expert$scenario == target$scenario & + expert$sample_size == target$sample_size & + expert$degree == 2 & + expert$scale == 1 & + expert$repair_lower == target$repair_lower & + expert$repair_upper == target$repair_upper & + expert$direction == + if (target$support == "one-sided") "lower" else "none", + ] + median_ise <- median(candidates$global_ise) + selected <- candidates[ + which.min(abs(candidates$global_ise - median_ise)), + ] + data.frame(target, replication = selected$replication) +}) +examples <- do.call(rbind, example_rows) + +dir.create(dirname(output_prefix), recursive = TRUE, showWarnings = FALSE) +write.csv(cell_ratios, paste0(output_prefix, "-cells.csv"), row.names = FALSE) +write.csv(family_ratios, paste0(output_prefix, "-families.csv"), row.names = FALSE) +write.csv(support_ratios, paste0(output_prefix, "-support.csv"), row.names = FALSE) +write.csv(activation, paste0(output_prefix, "-activation.csv"), row.names = FALSE) +write.csv(components, paste0(output_prefix, "-components.csv"), row.names = FALSE) +write.csv(examples, paste0(output_prefix, "-examples.csv"), row.names = FALSE) diff --git a/diagnostic/validate_native_boundary_experts.R b/diagnostic/validate_native_boundary_experts.R index c552caf..22c2e1d 100644 --- a/diagnostic/validate_native_boundary_experts.R +++ b/diagnostic/validate_native_boundary_experts.R @@ -29,14 +29,33 @@ integrate_values <- function(points, values) { sum(diff(points) * (values[-length(values)] + values[-1L]) / 2) } -fit_kde1d <- function(observations, xmin = NA_real_, xmax = NA_real_) { - arguments <- list(x = observations, xmin = xmin, xmax = xmax) +fit_kde1d <- function(observations, degree, + xmin = NA_real_, xmax = NA_real_) { + arguments <- list(x = observations, xmin = xmin, xmax = xmax, deg = degree) if (method != "pre-pr") { arguments$boundary_repair <- method == "expert" } do.call(kde1d, arguments) } +classify_finite_endpoint <- function(distances) { + distances <- sort(distances) + k <- min(length(distances) - 1L, ceiling(2 * sqrt(length(distances)))) + reference_distance <- distances[[k + 1L]] + if (!is.finite(reference_distance) || reference_distance <= 0) { + return(FALSE) + } + denominator <- sum(log( + reference_distance / + pmax(distances[seq_len(k)], .Machine$double.eps * reference_distance) + )) + if (!is.finite(denominator) || denominator <= 0) { + return(FALSE) + } + beta <- k / denominator + beta >= 0.9 && beta * (1 - qnorm(0.95) / sqrt(k)) <= 1 +} + one_sided <- list( exponential = list( random = function(n) rexp(n), @@ -74,6 +93,7 @@ two_sided <- list( beta_2_2 = c(2, 2) ) sample_sizes <- c(25L, 100L, 1000L, 2000L) +degrees <- 0:2 one_sided_scales <- c(1e-4, 1, 1e4) one_sided_directions <- c("lower", "upper") result_rows <- list() @@ -121,47 +141,55 @@ for (scenario_index in seq_along(one_sided)) { truth <- rev(scaled_truth) boundary <- points >= -scale * scenario$quantile(0.1) } - for (sample_size in sample_sizes) { - estimates <- matrix(NA_real_, length(points), replications) - for (replication in seq_len(replications)) { - set.seed(20260824L + 10000000L * scenario_index + - 1000000L * scale_index + 100000L * direction_index + - 1000L * match(sample_size, sample_sizes) + replication) - observations <- scale * scenario$random(sample_size) - if (direction == "lower") { - fit <- fit_kde1d(observations, xmin = 0) - } else { - fit <- fit_kde1d(-observations, xmax = 0) + for (degree in degrees) { + for (sample_size in sample_sizes) { + estimates <- matrix(NA_real_, length(points), replications) + for (replication in seq_len(replications)) { + # Reuse the base sample across scales and reflections so departures + # from scale/reflection equivariance are paired directly. + set.seed(20260824L + 10000000L * scenario_index + + 1000L * match(sample_size, sample_sizes) + replication) + observations <- scale * scenario$random(sample_size) + repair_endpoint <- classify_finite_endpoint(observations) + if (direction == "lower") { + fit <- fit_kde1d(observations, degree, xmin = 0) + } else { + fit <- fit_kde1d(-observations, degree, xmax = 0) + } + estimates[, replication] <- dkde1d(points, fit) + result_rows[[length(result_rows) + 1L]] <- data.frame( + support = "one-sided", + direction = direction, + scale = scale, + scenario = names(one_sided)[[scenario_index]], + degree = degree, + sample_size = sample_size, + replication = replication, + method = method, + repair_lower = direction == "lower" && repair_endpoint, + repair_upper = direction == "upper" && repair_endpoint, + global_ise = integrate_values( + points, (estimates[, replication] - truth)^2 + ), + boundary_ise = integrate_values( + points[boundary], + (estimates[boundary, replication] - truth[boundary])^2 + ), + edf = fit$edf, + loglik = fit$loglik + ) } - estimates[, replication] <- dkde1d(points, fit) - result_rows[[length(result_rows) + 1L]] <- data.frame( + summary_rows[[length(summary_rows) + 1L]] <- data.frame( support = "one-sided", direction = direction, scale = scale, scenario = names(one_sided)[[scenario_index]], + degree = degree, sample_size = sample_size, - replication = replication, method = method, - global_ise = integrate_values( - points, (estimates[, replication] - truth)^2 - ), - boundary_ise = integrate_values( - points[boundary], - (estimates[boundary, replication] - truth[boundary])^2 - ), - edf = fit$edf, - loglik = fit$loglik + as.list(summarize_estimates(points, estimates, truth, boundary)) ) } - summary_rows[[length(summary_rows) + 1L]] <- data.frame( - support = "one-sided", - direction = direction, - scale = scale, - scenario = names(one_sided)[[scenario_index]], - sample_size = sample_size, - method = method, - as.list(summarize_estimates(points, estimates, truth, boundary)) - ) } } } @@ -176,45 +204,53 @@ boundary <- points <= 0.1 | points >= 0.9 for (scenario_index in seq_along(two_sided)) { shapes <- two_sided[[scenario_index]] truth <- dbeta(points, shapes[[1L]], shapes[[2L]]) - for (sample_size in sample_sizes) { - estimates <- matrix(NA_real_, length(points), replications) - for (replication in seq_len(replications)) { - set.seed(20260825L + 100000L * scenario_index + - 1000L * match(sample_size, sample_sizes) + replication) - fit <- fit_kde1d( - rbeta(sample_size, shapes[[1L]], shapes[[2L]]), - xmin = 0, - xmax = 1 - ) - estimates[, replication] <- dkde1d(points, fit) - result_rows[[length(result_rows) + 1L]] <- data.frame( + for (degree in degrees) { + for (sample_size in sample_sizes) { + estimates <- matrix(NA_real_, length(points), replications) + for (replication in seq_len(replications)) { + set.seed(20260825L + 100000L * scenario_index + + 1000L * match(sample_size, sample_sizes) + replication) + observations <- rbeta(sample_size, shapes[[1L]], shapes[[2L]]) + fit <- fit_kde1d( + observations, + degree, + xmin = 0, + xmax = 1 + ) + estimates[, replication] <- dkde1d(points, fit) + result_rows[[length(result_rows) + 1L]] <- data.frame( + support = "two-sided", + direction = NA_character_, + scale = 1, + scenario = names(two_sided)[[scenario_index]], + degree = degree, + sample_size = sample_size, + replication = replication, + method = method, + repair_lower = classify_finite_endpoint(observations), + repair_upper = classify_finite_endpoint(1 - observations), + global_ise = integrate_values( + points, (estimates[, replication] - truth)^2 + ), + boundary_ise = integrate_values( + points[boundary], + (estimates[boundary, replication] - truth[boundary])^2 + ), + edf = fit$edf, + loglik = fit$loglik + ) + } + summary_rows[[length(summary_rows) + 1L]] <- data.frame( support = "two-sided", direction = NA_character_, scale = 1, scenario = names(two_sided)[[scenario_index]], + degree = degree, sample_size = sample_size, - replication = replication, method = method, - global_ise = integrate_values( - points, (estimates[, replication] - truth)^2 - ), - boundary_ise = integrate_values( - points[boundary], - (estimates[boundary, replication] - truth[boundary])^2 - ), - edf = fit$edf, - loglik = fit$loglik + as.list(summarize_estimates(points, estimates, truth, boundary)) ) } - summary_rows[[length(summary_rows) + 1L]] <- data.frame( - support = "two-sided", - direction = NA_character_, - scale = 1, - scenario = names(two_sided)[[scenario_index]], - sample_size = sample_size, - method = method, - as.list(summarize_estimates(points, estimates, truth, boundary)) - ) } } From 805abce9dccc79bfd64f1c9d8c4cb279a3b03aac Mon Sep 17 00:00:00 2001 From: tnagler Date: Mon, 24 Aug 2026 22:01:49 +0200 Subject: [PATCH 19/25] Fix strict compiler conversion warnings --- include/kde1d/kde1d.hpp | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 0cb77fa..3adc043 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -1121,7 +1121,9 @@ Kde1d::select_boundary_bandwidth(const EndpointData& endpoint, const Eigen::Index n_bw = std::min( dist.size(), std::max( - 4, static_cast(std::ceil(fraction * dist.size())))); + 4, + static_cast( + std::ceil(fraction * static_cast(dist.size()))))); bandwidth::PluginBandwidthSelector selector(dist.head(n_bw), weights.head(n_bw)); return selector.select_bandwidth(2) * multiplier_; @@ -1259,7 +1261,8 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, for (Eigen::Index j = 0; j < eval_dist.size(); ++j) { const double a = eval_dist(j) / h; const BoundaryKernelCoefficients c = boundary_kernel_coefficients(a); - const double position = eval_dist(j) * num_bins / convolutions.upper; + const double position = + eval_dist(j) * static_cast(num_bins) / convolutions.upper; const size_t bin = std::min(static_cast(position), num_bins - 1); const double fraction = position - static_cast(bin); auto interpolate = [&](const Eigen::VectorXd& values) { From ba10d49695b005473b12170d5e7f4390639a641c Mon Sep 17 00:00:00 2001 From: tnagler Date: Wed, 26 Aug 2026 13:15:44 +0200 Subject: [PATCH 20/25] Use biweight boundary fusion --- diagnostic/PR_COMMENT.md | 4 ++-- docs/overview-continuous.dox | 4 ++-- include/kde1d/kde1d.hpp | 4 ++-- test/test.cpp | 6 +++--- 4 files changed, 9 insertions(+), 9 deletions(-) diff --git a/diagnostic/PR_COMMENT.md b/diagnostic/PR_COMMENT.md index 9ee0435..dc26734 100644 --- a/diagnostic/PR_COMMENT.md +++ b/diagnostic/PR_COMMENT.md @@ -47,10 +47,10 @@ Let $F_B$ be the normalized bulk CDF, $$ q=\min(1/4,n_e^{-1/2}), \qquad -g(p)=1-3\min(1,p/q)^2+2\min(1,p/q)^3. +g(p)=\{1-\min(1,p/q)^2\}^2. $$ -Selected lower and upper experts receive weights +Selected lower and upper experts receive the biweight fusion weights $w_L(x)=g\{F_B(x)\}$ and $w_U(x)=g\{1-F_B(x)\}$, giving $$ diff --git a/docs/overview-continuous.dox b/docs/overview-continuous.dox index c3bd932..db7e4b5 100644 --- a/docs/overview-continuous.dox +++ b/docs/overview-continuous.dox @@ -83,10 +83,10 @@ Let @f$F_B@f$ be the normalized bulk CDF and @f[ q=\min(1/4,n_e^{-1/2}), \qquad -g(p)=1-3\min(1,p/q)^2+2\min(1,p/q)^3. +g(p)=\{1-\min(1,p/q)^2\}^2. @f] -For selected lower and upper endpoints, the fusion weights are +For selected lower and upper endpoints, the biweight fusion weights are @f$w_L(x)=g\{F_B(x)\}@f$ and @f$w_U(x)=g\{1-F_B(x)\}@f$; a missing or rejected endpoint has weight zero. The final density before numerical normalization is diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 3adc043..7669aad 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -1342,7 +1342,7 @@ Kde1d::fuse_boundary_components(const Eigen::VectorXd& grid, //! @f[ //! \begin{align*} //! q &= \min(1/4,n_e^{-1/2}), & z(p) &= \min(1,p/q), \\[2pt] -//! g(p) &= 1-3z(p)^2+2z(p)^3, \\[2pt] +//! g(p) &= \{1-z(p)^2\}^2, \\[2pt] //! w_L &= g(F_B), & w_U &= g(1-F_B), \\[2pt] //! \widehat f //! &= w_L\widehat f_L+(1-w_L-w_U)\widehat f_B+w_U\widehat f_U, \\[2pt] @@ -1384,7 +1384,7 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, const double q = std::min(0.25, 1.0 / std::sqrt(n_eff)); auto endpoint_weight = [&](double probability) { const double z = std::min(1.0, probability / q); - return 1.0 - (3.0 * z * z - 2.0 * z * z * z); + return (1.0 - z * z) * (1.0 - z * z); }; // Only evaluate endpoint fits where their fusion weights are nonzero. diff --git a/test/test.cpp b/test/test.cpp index 9b58f6a..9116359 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -150,8 +150,8 @@ TEST_CASE("one-sided finite endpoints use the boundary expert", CHECK(fit.get_values().isApprox(manual.get_values(), 1e-12)); Eigen::VectorXd expected_density(6); - expected_density << 0.9884817, 0.9885018, 0.9865198, 0.9465577, 0.7315411, - 0.0077367; + expected_density << 0.9883801, 0.9883894, 0.9865788, 0.9497592, 0.7314455, + 0.0077357; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(4), fit.get_values()(24), fit.get_values()(49), fit.get_values()(99), @@ -250,7 +250,7 @@ TEST_CASE("two-sided endpoints are classified independently", fit.fit(observations); Eigen::VectorXd expected_density(6); - expected_density << 1.9984196, 1.9944352, 1.9846050, 0.9946111, 0.0562112, + expected_density << 1.9986281, 1.9954211, 1.9825467, 0.9946342, 0.0562125, 0.0000020; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(49), From acf0f32f458a2dabd3e09064c165f383157f62dd Mon Sep 17 00:00:00 2001 From: tnagler Date: Wed, 26 Aug 2026 13:35:05 +0200 Subject: [PATCH 21/25] Use local-linear boundary repair --- diagnostic/PR_COMMENT.md | 16 ++++---- docs/overview-continuous.dox | 10 ++--- include/kde1d/kde1d.hpp | 80 +++++++++++++----------------------- test/test.cpp | 6 +-- 4 files changed, 44 insertions(+), 68 deletions(-) diff --git a/diagnostic/PR_COMMENT.md b/diagnostic/PR_COMMENT.md index dc26734..d93ecfa 100644 --- a/diagnostic/PR_COMMENT.md +++ b/diagnostic/PR_COMMENT.md @@ -29,17 +29,12 @@ $$ Endpoints consistent with a finite nonzero limiting density receive a boundary expert. Exploding, vanishing, ambiguous, and degenerate endpoints retain the -bulk. The expert is the equal average +bulk. The expert is a Gaussian local-linear equivalent-kernel estimate, -$$ -\widehat f_E=(\widehat f_{\mathrm{local\ linear}} - +\widehat f_{\mathrm{local\ quadratic}})/2 -$$ - -of Gaussian equivalent-kernel estimates. Both kernels share an automatically -selected degree-2 plug-in bandwidth on the original scale, using all +using an automatically selected degree-2 plug-in bandwidth on the original +scale. The selector uses all positive-weight observations on bounded support and the closest 75% by row -count on one-sided support. The three required Gaussian convolutions are +count on one-sided support. The two required Gaussian convolutions are evaluated on a shared 256-bin FFT grid. Let $F_B$ be the normalized bulk CDF, @@ -67,6 +62,9 @@ clamps, and normalization fixed. ## Validation design +The large-scale tables below predate the biweight and local-linear +simplifications and will be refreshed before merge. + The primary benchmark is the actual pre-PR package at parent commit `7faec53` with C++ commit `b16d514`: log transform for one-sided support and probit for two-sided support. The experiment used 200 paired replications for diff --git a/docs/overview-continuous.dox b/docs/overview-continuous.dox index db7e4b5..6602539 100644 --- a/docs/overview-continuous.dox +++ b/docs/overview-continuous.dox @@ -63,16 +63,16 @@ Weighted fits use effective counts and the more conservative lower threshold behavior retains the bulk fit. Setting `boundary_repair=false` skips the classifier and all expert calculations. -For a selected endpoint, the expert is the equal average of Gaussian -local-linear and local-quadratic equivalent-kernel estimates on the original -scale. Both use one automatically selected degree-two plug-in bandwidth. On -two-sided support the selector uses all positive-weight observations; on +For a selected endpoint, the expert is a Gaussian local-linear +equivalent-kernel estimate on the original scale. It uses an automatically +selected degree-two plug-in bandwidth. On two-sided support the selector uses +all positive-weight observations; on one-sided support it uses the closest 75% by row count. Public case weights enter the expert estimand and bandwidth selector. A manual bulk `bandwidth` does not replace this expert bandwidth, while `multiplier` scales both. The equivalent kernel is expressed as a pointwise combination of an ordinary -Gaussian KDE and its first two derivatives. These three convolutions are +Gaussian KDE and its first derivative. These two convolutions are evaluated on a 256-bin FFT grid. Invalid or nonpositive local-polynomial values are set to zero before fusion. diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 7669aad..13dc99f 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -20,8 +20,8 @@ enum class VarType //! //! Continuous fits use a transformed local-likelihood estimate as their bulk //! component. When `boundary_repair` is enabled, finite support endpoints may -//! additionally use a nonnegative blend of local-linear and local-quadratic -//! boundary kernels. See @ref overview-continuous for the transforms, +//! additionally use a nonnegative local-linear boundary kernel. See +//! @ref overview-continuous for the transforms, //! endpoint classifier, bandwidths, fusion weights, and EDF approximation. class Kde1d { @@ -157,18 +157,14 @@ class Kde1d { Eigen::VectorXd f0; Eigen::VectorXd f1; - Eigen::VectorXd f2; Eigen::VectorXd influence_weight; double upper{ 0.0 }; }; struct BoundaryKernelCoefficients { - double c10; - double c11; - double c20; - double c21; - double c22; + double c0; + double c1; }; // data members @@ -1129,7 +1125,7 @@ Kde1d::select_boundary_bandwidth(const EndpointData& endpoint, return selector.select_bandwidth(2) * multiplier_; } -//! Computes the ordinary Gaussian KDE and its first two derivatives on the +//! Computes the ordinary Gaussian KDE and its first derivative on the //! regular FFT grid used by a boundary component. The influence weights are //! the average normalized case weights in the same bins. //! @param dist ordered endpoint distances. @@ -1163,7 +1159,6 @@ Kde1d::compute_boundary_convolutions(const Eigen::VectorXd& dist, const double scale = fft_weight / weights.sum(); convolutions.f0 = scale * kde_fft.kde_drv(0); convolutions.f1 = scale * kde_fft.kde_drv(1); - convolutions.f2 = scale * kde_fft.kde_drv(2); convolutions.influence_weight = Eigen::VectorXd::Ones(num_bins + 1); if (weights.minCoeff() != weights.maxCoeff()) { const Eigen::VectorXd count = tools::linbin(dist.head(n_fft), @@ -1180,10 +1175,10 @@ Kde1d::compute_boundary_convolutions(const Eigen::VectorXd& dist, return convolutions; } -//! Computes the first inverse-moment rows for degree-one and degree-two -//! Gaussian boundary kernels at standardized endpoint distance @f$a@f$. +//! Computes the first inverse-moment row for the local-linear Gaussian +//! boundary kernel at standardized endpoint distance @f$a@f$. //! @param a endpoint distance divided by bandwidth. -//! @return coefficients @f$c_{10},c_{11},c_{20},c_{21},c_{22}@f$. +//! @return coefficients @f$c_0,c_1@f$. inline Kde1d::BoundaryKernelCoefficients Kde1d::boundary_kernel_coefficients(double a) const { @@ -1191,50 +1186,35 @@ Kde1d::boundary_kernel_coefficients(double a) const const double mu0 = 0.5 * std::erfc(-a * 0.7071067811865475); const double mu1 = -phi; const double mu2 = mu0 - a * phi; - const double mu3 = -(a * a + 2.0) * phi; - const double mu4 = 3.0 * mu0 - (a * a * a + 3.0 * a) * phi; - const double det1 = mu0 * mu2 - mu1 * mu1; - const double det2 = mu0 * (mu2 * mu4 - mu3 * mu3) - - mu1 * (mu1 * mu4 - mu2 * mu3) + - mu2 * (mu1 * mu3 - mu2 * mu2); - return { mu2 / det1, - -mu1 / det1, - (mu2 * mu4 - mu3 * mu3) / det2, - (mu2 * mu3 - mu1 * mu4) / det2, - (mu1 * mu3 - mu2 * mu2) / det2 }; + const double denom = mu0 * mu2 - mu1 * mu1; + return { mu2 / denom, -mu1 / denom }; } -//! Fits the average of Gaussian local-linear and local-quadratic equivalent -//! kernels from sample distances @f$d@f$ to endpoint-distance grid @f$t@f$. -//! For degree @f$p@f$, shared bandwidth @f$h@f$, truncated Gaussian moments -//! @f$\mu_r(a)@f$, and @f$M_p(a)=[\mu_{j+k}(a)]_{j,k=0}^p@f$, +//! Fits a Gaussian local-linear equivalent kernel from sample distances +//! @f$d@f$ to endpoint-distance grid @f$t@f$. For bandwidth @f$h@f$, +//! truncated Gaussian moments @f$\mu_r(a)@f$, and +//! @f$M(a)=[\mu_{j+k}(a)]_{j,k=0}^1@f$, //! @f[ //! \begin{align*} //! a &= t/h, & u_i &= (t-d_i)/h, \\[2pt] -//! \widehat f_p(t;h) +//! \widehat f_E(t;h) //! &= \frac{1}{nh}\sum_{i=1}^n w_i\phi(u_i)\, -//! e_0^\mathsf{T}M_p(a)^{-1} -//! (1,u_i,\ldots,u_i^p)^\mathsf{T}, \\[2pt] -//! \widehat f_\partial(t) -//! &= \{\widehat f_1(t;h)+\widehat f_2(t;h)\}/2. +//! e_0^\mathsf{T}M(a)^{-1}(1,u_i)^\mathsf{T}. //! \end{align*} //! @f] -//! Writing @f$f^{(r)}@f$ for the @f$r@f$th derivative of the ordinary -//! Gaussian KDE and @f$c_{pj}@f$ for the entries of the first row of -//! @f$M_p(a)^{-1}@f$, the same estimator is +//! Writing @f$f^{(1)}@f$ for the first derivative of the ordinary Gaussian KDE +//! and @f$(c_0,c_1)=e_0^\mathsf{T}M(a)^{-1}@f$, the same estimator is //! @f[ //! \begin{align*} -//! \widehat f_\partial(t) -//! &= \frac{1}{2}\{(c_{10}+c_{20}+c_{22})f(t) -//! -h(c_{11}+c_{21})f^{(1)}(t)+h^2c_{22}f^{(2)}(t)\}. +//! \widehat f_E(t;h) &= c_0f(t)-hc_1f^{(1)}(t). //! \end{align*} //! @f] -//! This identity evaluates the three convolutions by FFT. -//! Both kernels use the same normalized case weights @f$w_i@f$. The returned -//! influence numerator is the corresponding average diagonal contribution. +//! This identity evaluates the two convolutions by FFT. The returned influence +//! numerator is the diagonal contribution with normalized case weights +//! @f$w_i@f$. //! @param dist ordered distances of the observations from the support endpoint. //! @param eval_dist endpoint distances at which to evaluate the component. -//! @param bandwidth shared bandwidth of both equivalent kernels. +//! @param bandwidth bandwidth of the equivalent kernel. //! @param weights correspondingly ordered case weights with mean one. //! @return the density and influence numerator on `eval_dist`. inline Kde1d::BoundaryComponent @@ -1268,13 +1248,11 @@ Kde1d::fit_boundary_component(const Eigen::VectorXd& dist, auto interpolate = [&](const Eigen::VectorXd& values) { return (1.0 - fraction) * values(bin) + fraction * values(bin + 1); }; - fit.density(j) = - 0.5 * ((c.c10 + c.c20 + c.c22) * interpolate(convolutions.f0) - - h * (c.c11 + c.c21) * interpolate(convolutions.f1) + - h * h * c.c22 * interpolate(convolutions.f2)); + fit.density(j) = c.c0 * interpolate(convolutions.f0) - + h * c.c1 * interpolate(convolutions.f1); fit.influence_num(j) = - K0_ * (c.c10 + c.c20) * interpolate(convolutions.influence_weight) / - (2.0 * static_cast(dist.size()) * h); + K0_ * c.c0 * interpolate(convolutions.influence_weight) / + (static_cast(dist.size()) * h); } // Remove unstable local-polynomial values. @@ -1334,8 +1312,8 @@ Kde1d::fuse_boundary_components(const Eigen::VectorXd& grid, //! Fuses the transformed bulk density @f$\widehat f_B@f$ with endpoint //! densities @f$\widehat f_L@f$ and @f$\widehat f_U@f$. Each endpoint density -//! averages local-linear and local-quadratic kernels using one degree-2 -//! bandwidth, selected from all distances on bounded support and the closest +//! uses a local-linear kernel with a degree-2 plug-in bandwidth, selected from +//! all distances on bounded support and the closest //! 75% of positive-weight observations on one-sided support. Smooth weights //! @f$w_L@f$ and @f$w_U@f$ are functions of the weighted bulk CDF and shrink //! with effective sample size @f$n_e@f$: diff --git a/test/test.cpp b/test/test.cpp index 9116359..f1a3ab6 100644 --- a/test/test.cpp +++ b/test/test.cpp @@ -150,8 +150,8 @@ TEST_CASE("one-sided finite endpoints use the boundary expert", CHECK(fit.get_values().isApprox(manual.get_values(), 1e-12)); Eigen::VectorXd expected_density(6); - expected_density << 0.9883801, 0.9883894, 0.9865788, 0.9497592, 0.7314455, - 0.0077357; + expected_density << 0.9797951, 0.9798032, 0.9780643, 0.9448344, 0.7316556, + 0.0077380; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(4), fit.get_values()(24), fit.get_values()(49), fit.get_values()(99), @@ -250,7 +250,7 @@ TEST_CASE("two-sided endpoints are classified independently", fit.fit(observations); Eigen::VectorXd expected_density(6); - expected_density << 1.9986281, 1.9954211, 1.9825467, 0.9946342, 0.0562125, + expected_density << 1.9985571, 1.9950070, 1.9824915, 0.9946390, 0.0562128, 0.0000020; Eigen::VectorXd selected_density(6); selected_density << fit.get_values()(0), fit.get_values()(49), From bf7484d91e87a32ddeadf7d4c4a273b7f248f47c Mon Sep 17 00:00:00 2001 From: tnagler Date: Wed, 26 Aug 2026 13:40:56 +0200 Subject: [PATCH 22/25] Clarify boundary bandwidth documentation --- diagnostic/PR_COMMENT.md | 2 +- docs/overview-continuous.dox | 2 +- include/kde1d/kde1d.hpp | 6 +++--- 3 files changed, 5 insertions(+), 5 deletions(-) diff --git a/diagnostic/PR_COMMENT.md b/diagnostic/PR_COMMENT.md index d93ecfa..d3e630c 100644 --- a/diagnostic/PR_COMMENT.md +++ b/diagnostic/PR_COMMENT.md @@ -31,7 +31,7 @@ Endpoints consistent with a finite nonzero limiting density receive a boundary expert. Exploding, vanishing, ambiguous, and degenerate endpoints retain the bulk. The expert is a Gaussian local-linear equivalent-kernel estimate, -using an automatically selected degree-2 plug-in bandwidth on the original +using an automatically selected bandwidth on the original scale. The selector uses all positive-weight observations on bounded support and the closest 75% by row count on one-sided support. The two required Gaussian convolutions are diff --git a/docs/overview-continuous.dox b/docs/overview-continuous.dox index 6602539..8a46cb8 100644 --- a/docs/overview-continuous.dox +++ b/docs/overview-continuous.dox @@ -65,7 +65,7 @@ classifier and all expert calculations. For a selected endpoint, the expert is a Gaussian local-linear equivalent-kernel estimate on the original scale. It uses an automatically -selected degree-two plug-in bandwidth. On two-sided support the selector uses +selected bandwidth. On two-sided support the selector uses all positive-weight observations; on one-sided support it uses the closest 75% by row count. Public case weights enter the expert estimand and bandwidth selector. A manual bulk `bandwidth` diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 13dc99f..54d4e54 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -1099,7 +1099,7 @@ Kde1d::prepare_endpoint(const Eigen::VectorXd& x, //! closest `fraction` of positive-weight observations are used by row count. //! @param endpoint sorted endpoint distances and case weights. //! @param fraction fraction of positive-weight observations used for selection. -//! @return degree-two plug-in bandwidth after applying the public multiplier. +//! @return selected boundary bandwidth after applying the public multiplier. inline double Kde1d::select_boundary_bandwidth(const EndpointData& endpoint, double fraction) const @@ -1312,7 +1312,7 @@ Kde1d::fuse_boundary_components(const Eigen::VectorXd& grid, //! Fuses the transformed bulk density @f$\widehat f_B@f$ with endpoint //! densities @f$\widehat f_L@f$ and @f$\widehat f_U@f$. Each endpoint density -//! uses a local-linear kernel with a degree-2 plug-in bandwidth, selected from +//! uses a local-linear kernel with an automatically selected bandwidth, based on //! all distances on bounded support and the closest //! 75% of positive-weight observations on one-sided support. Smooth weights //! @f$w_L@f$ and @f$w_U@f$ are functions of the weighted bulk CDF and shrink @@ -1378,7 +1378,7 @@ Kde1d::repair_boundaries(const Eigen::VectorXd& x, const Eigen::Index n_lower = (w_l.array() > 0.0).count(); const Eigen::Index n_upper = (w_u.array() > 0.0).count(); - // Reflection invariance gives both endpoints the same degree-2 bandwidth. + // Reflection invariance gives both endpoints the same boundary bandwidth. const double bandwidth_fraction = (!std::isnan(xmin_) && !std::isnan(xmax_)) ? 1.0 : 0.75; const EndpointData& bandwidth_endpoint = From 2c809d4132e0ce1210acb5d5da5a8b69d4937044 Mon Sep 17 00:00:00 2001 From: tnagler Date: Wed, 26 Aug 2026 14:02:47 +0200 Subject: [PATCH 23/25] Document Box-Cox boundary transform --- docs/overview-continuous.dox | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/docs/overview-continuous.dox b/docs/overview-continuous.dox index 8a46cb8..4d3dc0e 100644 --- a/docs/overview-continuous.dox +++ b/docs/overview-continuous.dox @@ -18,7 +18,8 @@ z(x)=\Phi^{-1}\left(\frac{x-a+5\times10^{-5}R}{1.0001R}\right). If exactly one endpoint is finite, let @f$d(x)@f$ denote distance from it. The scale @f$s@f$ is the weighted median of the observed distances, with a maximum-distance and unit fallback for degenerate samples, and -@f$\epsilon=10^{-5}s@f$. The one-sided transform is +@f$\epsilon=10^{-5}s@f$. The one-sided transform is an endpoint-anchored, +scaled member of the Box-Cox family with power parameter @f$\lambda=1/4@f$: @f[ z(x)=4\left[\left\{\frac{\epsilon+d(x)}{s}\right\}^{1/4} @@ -28,7 +29,7 @@ z(x)=4\left[\left\{\frac{\epsilon+d(x)}{s}\right\}^{1/4} =\frac{1}{s}\left\{\frac{\epsilon+d(x)}{s}\right\}^{-3/4}. @f] -The fourth-root transform and its Jacobian are scale equivariant. The small +This Box-Cox transform and its Jacobian are scale equivariant. The small offset keeps the transformed endpoint finite. Density values are transformed back to the original scale and normalized on the interpolation grid. From d1738841ca141212ceea650b2c22c128fa179563 Mon Sep 17 00:00:00 2001 From: tnagler Date: Wed, 26 Aug 2026 13:46:55 +0200 Subject: [PATCH 24/25] Correct probit Jacobian factor --- include/kde1d/kde1d.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/kde1d/kde1d.hpp b/include/kde1d/kde1d.hpp index 54d4e54..1311efa 100644 --- a/include/kde1d/kde1d.hpp +++ b/include/kde1d/kde1d.hpp @@ -935,7 +935,7 @@ Kde1d::boundary_correct(const Eigen::VectorXd& x, const Eigen::VectorXd& fhat) auto rng = xmax_ - xmin_; corr_term = (x.array() - xmin_ + 5e-5 * rng) / (xmax_ - xmin_ + 1e-4 * rng); corr_term = stats::dnorm(stats::qnorm(corr_term)); - corr_term /= (xmax_ - xmin_ + 1e-4 * rng); + corr_term *= (xmax_ - xmin_ + 1e-4 * rng); corr_term = 1.0 / corr_term.array(); } else if (!std::isnan(xmin_)) { // left boundary -> fourth-root-transform Jacobian From fa9fc4a939db38026faae6c8418a8d47a138ae88 Mon Sep 17 00:00:00 2001 From: tnagler Date: Wed, 26 Aug 2026 14:02:56 +0200 Subject: [PATCH 25/25] Refresh boundary validation results --- diagnostic/PR_COMMENT.md | 160 +++++++++++++++---------------- diagnostic/boundary-examples.png | Bin 170831 -> 169415 bytes 2 files changed, 80 insertions(+), 80 deletions(-) diff --git a/diagnostic/PR_COMMENT.md b/diagnostic/PR_COMMENT.md index d3e630c..a2d0fdd 100644 --- a/diagnostic/PR_COMMENT.md +++ b/diagnostic/PR_COMMENT.md @@ -4,19 +4,21 @@ This PR changes continuous fits with known finite support in two steps. For a one-sided support, write $d(x)$ for distance from the finite endpoint, let $s$ be the weighted median observed distance, and set -$\epsilon=10^{-5}s$. The transformed bulk estimator now uses +$\epsilon=10^{-5}s$. The transformed bulk estimator uses an endpoint-anchored, +scaled member of the Box-Cox family with power parameter $\lambda=1/4$: $$ T\{d(x)\} -=4\left[\left\{\frac{d(x)+\epsilon}{s}\right\}^{1/4} --\left(\frac{\epsilon}{s}\right)^{1/4}\right], +=4[\{\frac{d(x)+\epsilon}{s}\}^{1/4} +-\{\frac{\epsilon}{s}\}^{1/4}], \qquad |T'(x)| -=\frac{1}{s}\left\{\frac{d(x)+\epsilon}{s}\right\}^{-3/4}. +=\frac{1}{s}\{\frac{d(x)+\epsilon}{s}\}^{-3/4}. $$ -This replaces the previous log transform and makes the construction scale -equivariant. Two-sided fits retain the regularized probit bulk transform. +This Box-Cox transform replaces the previous log transform and makes the +construction scale equivariant. Two-sided fits retain the regularized probit +bulk transform. Each finite endpoint is then classified independently from its first $k\simeq2\sqrt{n_e}$ order statistics. In the unweighted case, @@ -29,10 +31,8 @@ $$ Endpoints consistent with a finite nonzero limiting density receive a boundary expert. Exploding, vanishing, ambiguous, and degenerate endpoints retain the -bulk. The expert is a Gaussian local-linear equivalent-kernel estimate, - -using an automatically selected bandwidth on the original -scale. The selector uses all +bulk. The expert is a Gaussian local-linear equivalent-kernel estimate with an +automatically selected bandwidth on the original scale. The selector uses all positive-weight observations on bounded support and the closest 75% by row count on one-sided support. The two required Gaussian convolutions are evaluated on a shared 256-bin FFT grid. @@ -62,8 +62,8 @@ clamps, and normalization fixed. ## Validation design -The large-scale tables below predate the biweight and local-linear -simplifications and will be refreshed before merge. +> **Before merging:** remove `diagnostic/`; it is retained in this branch only +> to make the PR validation reproducible during review. The primary benchmark is the actual pre-PR package at parent commit `7faec53` with C++ commit `b16d514`: log transform for one-sided support and probit for @@ -85,28 +85,28 @@ PR**. Parentheses are paired Monte Carlo standard errors. | support | degree | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:|---:| -| one-sided | 0 | 0.748 (0.044) | 0.579 (0.028) | 0.513 (0.011) | 0.475 (0.010) | -| one-sided | 1 | 0.505 (0.020) | 0.411 (0.011) | 0.684 (0.063) | 0.724 (0.050) | -| one-sided | 2 | 0.211 (0.036) | 0.198 (0.021) | 0.208 (0.018) | 0.260 (0.015) | -| two-sided | 0 | 0.951 (0.005) | 0.943 (0.005) | 0.941 (0.006) | 0.925 (0.005) | -| two-sided | 1 | 0.867 (0.006) | 0.823 (0.007) | 0.847 (0.005) | 0.852 (0.004) | -| two-sided | 2 | 0.892 (0.013) | 0.911 (0.006) | 0.940 (0.006) | 0.932 (0.006) | +| one-sided | 0 | 1.810 (0.116) | 1.134 (0.049) | 0.586 (0.015) | 0.519 (0.011) | +| one-sided | 1 | 0.789 (0.038) | 0.508 (0.011) | 0.566 (0.042) | 0.612 (0.037) | +| one-sided | 2 | 0.550 (0.034) | 0.394 (0.015) | 0.231 (0.008) | 0.231 (0.008) | +| two-sided | 0 | 0.946 (0.005) | 0.940 (0.005) | 0.943 (0.006) | 0.926 (0.006) | +| two-sided | 1 | 0.856 (0.007) | 0.817 (0.007) | 0.846 (0.005) | 0.850 (0.004) | +| two-sided | 2 | 0.881 (0.013) | 0.906 (0.006) | 0.943 (0.007) | 0.932 (0.007) | ### Boundary ratio, averaged over families | support | degree | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:|---:| -| one-sided | 0 | 0.702 (0.049) | 0.513 (0.030) | 0.447 (0.013) | 0.399 (0.011) | -| one-sided | 1 | 0.399 (0.022) | 0.303 (0.011) | 0.636 (0.075) | 0.702 (0.059) | -| one-sided | 2 | 0.144 (0.027) | 0.151 (0.027) | 0.159 (0.016) | 0.205 (0.015) | -| two-sided | 0 | 0.923 (0.005) | 0.944 (0.005) | 0.954 (0.005) | 0.939 (0.005) | -| two-sided | 1 | 0.824 (0.008) | 0.826 (0.007) | 0.879 (0.004) | 0.877 (0.004) | -| two-sided | 2 | 0.883 (0.012) | 0.913 (0.005) | 0.955 (0.005) | 0.945 (0.005) | - -The expert also improves over the unrepaired new bulk. Averaged global ISE -ratios range from 0.84--0.94 for degree 0, 0.74--0.89 for degree 1, and -0.88--0.92 for degree 2 on one-sided support. The corresponding bounded ratios -are 0.93--0.95, 0.82--0.87, and 0.89--0.94. +| one-sided | 0 | 3.149 (0.278) | 1.553 (0.097) | 0.563 (0.020) | 0.461 (0.014) | +| one-sided | 1 | 0.931 (0.073) | 0.437 (0.017) | 0.519 (0.047) | 0.590 (0.042) | +| one-sided | 2 | 0.612 (0.048) | 0.396 (0.024) | 0.190 (0.009) | 0.190 (0.008) | +| two-sided | 0 | 0.918 (0.005) | 0.939 (0.005) | 0.955 (0.006) | 0.940 (0.006) | +| two-sided | 1 | 0.817 (0.009) | 0.821 (0.007) | 0.878 (0.004) | 0.876 (0.004) | +| two-sided | 2 | 0.877 (0.012) | 0.910 (0.005) | 0.958 (0.006) | 0.946 (0.006) | + +Against the unrepaired new bulk, averaged global ISE ratios range from +0.83--0.94 for degree 0, 0.73--0.88 for degree 1, and 0.87--0.92 for degree 2 +on one-sided support. The corresponding bounded ratios are 0.93--0.95, +0.82--0.86, and 0.88--0.94.
Family-level global / boundary ISE ratios @@ -115,78 +115,78 @@ are 0.93--0.95, 0.82--0.87, and 0.89--0.94. | family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:| -| Exponential | 0.75 / 0.73 | 0.49 / 0.45 | 0.37 / 0.30 | 0.34 / 0.27 | -| Gamma$(0.75)$ | 0.55 / 0.54 | 0.51 / 0.50 | 0.45 / 0.44 | 0.44 / 0.43 | -| Gamma$(2)$ | 0.71 / 0.52 | 0.76 / 0.58 | 0.81 / 0.69 | 0.80 / 0.67 | -| half-normal | 0.46 / 0.38 | 0.41 / 0.32 | 0.31 / 0.21 | 0.28 / 0.17 | -| Lomax$(2)$ | 1.28 / 1.34 | 0.72 / 0.70 | 0.63 / 0.59 | 0.51 / 0.45 | +| Exponential | 1.48 / 2.67 | 1.36 / 2.41 | 0.58 / 0.56 | 0.51 / 0.45 | +| Gamma$(0.75)$ | 2.05 / 2.76 | 0.91 / 0.97 | 0.33 / 0.32 | 0.28 / 0.27 | +| Gamma$(2)$ | 0.79 / 0.66 | 0.84 / 0.75 | 0.87 / 0.80 | 0.86 / 0.77 | +| half-normal | 0.88 / 1.28 | 0.79 / 1.08 | 0.54 / 0.53 | 0.46 / 0.38 | +| Lomax$(2)$ | 3.84 / 8.37 | 1.77 / 2.56 | 0.61 / 0.60 | 0.50 / 0.44 | #### One-sided, degree 1 | family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:| -| Exponential | 0.49 / 0.37 | 0.31 / 0.22 | 0.38 / 0.26 | 0.38 / 0.27 | -| Gamma$(0.75)$ | 0.27 / 0.25 | 0.25 / 0.21 | 0.45 / 0.43 | 0.53 / 0.52 | -| Gamma$(2)$ | 0.69 / 0.46 | 0.81 / 0.63 | 0.93 / 0.98 | 1.01 / 1.19 | -| half-normal | 0.45 / 0.32 | 0.38 / 0.23 | 0.43 / 0.25 | 0.43 / 0.25 | -| Lomax$(2)$ | 0.62 / 0.60 | 0.31 / 0.22 | 1.23 / 1.26 | 1.27 / 1.28 | +| Exponential | 0.70 / 0.83 | 0.47 / 0.43 | 0.37 / 0.25 | 0.35 / 0.24 | +| Gamma$(0.75)$ | 0.72 / 0.88 | 0.33 / 0.30 | 0.32 / 0.30 | 0.36 / 0.34 | +| Gamma$(2)$ | 0.74 / 0.59 | 0.84 / 0.73 | 0.93 / 1.03 | 1.00 / 1.21 | +| half-normal | 0.61 / 0.65 | 0.50 / 0.40 | 0.47 / 0.29 | 0.44 / 0.26 | +| Lomax$(2)$ | 1.17 / 1.71 | 0.40 / 0.32 | 0.74 / 0.72 | 0.91 / 0.90 | #### One-sided, degree 2 | family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:| -| Exponential | 0.07 / 0.04 | 0.02 / 0.01 | 0.06 / 0.04 | 0.09 / 0.06 | -| Gamma$(0.75)$ | 0.03 / 0.03 | 0.04 / 0.03 | 0.23 / 0.21 | 0.23 / 0.21 | -| Gamma$(2)$ | 0.38 / 0.18 | 0.72 / 0.56 | 0.59 / 0.44 | 0.62 / 0.50 | -| half-normal | 0.09 / 0.04 | 0.03 / 0.02 | 0.03 / 0.01 | 0.06 / 0.03 | -| Lomax$(2)$ | 0.49 / 0.43 | 0.17 / 0.13 | 0.13 / 0.09 | 0.30 / 0.23 | +| Exponential | 0.43 / 0.53 | 0.32 / 0.38 | 0.10 / 0.07 | 0.10 / 0.07 | +| Gamma$(0.75)$ | 0.47 / 0.56 | 0.18 / 0.17 | 0.12 / 0.11 | 0.10 / 0.10 | +| Gamma$(2)$ | 0.61 / 0.48 | 0.84 / 0.83 | 0.67 / 0.59 | 0.67 / 0.61 | +| half-normal | 0.37 / 0.42 | 0.32 / 0.32 | 0.16 / 0.10 | 0.13 / 0.06 | +| Lomax$(2)$ | 0.87 / 1.09 | 0.30 / 0.28 | 0.11 / 0.08 | 0.15 / 0.11 | #### Two-sided, degree 0 | family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:| -| Beta$(0.75,0.75)$ | 1.02 / 1.03 | 1.03 / 1.04 | 1.04 / 1.04 | 1.05 / 1.05 | -| Beta$(0.75,2)$ | 0.99 / 0.98 | 1.01 / 1.00 | 1.07 / 1.07 | 1.06 / 1.06 | -| Beta$(1,2)$ | 0.93 / 0.91 | 0.85 / 0.86 | 0.83 / 0.86 | 0.78 / 0.81 | -| Beta$(2,0.75)$ | 1.00 / 0.99 | 1.01 / 1.00 | 1.09 / 1.08 | 1.06 / 1.05 | -| Beta$(2,1)$ | 0.95 / 0.93 | 0.89 / 0.89 | 0.78 / 0.81 | 0.79 / 0.82 | -| Beta$(2,2)$ | 0.82 / 0.65 | 0.94 / 0.88 | 1.00 / 1.00 | 1.00 / 1.00 | -| Uniform | 0.95 / 0.98 | 0.88 / 0.93 | 0.77 / 0.82 | 0.74 / 0.79 | +| Beta$(0.75,0.75)$ | 1.01 / 1.02 | 1.03 / 1.04 | 1.05 / 1.05 | 1.06 / 1.06 | +| Beta$(0.75,2)$ | 0.98 / 0.97 | 1.01 / 1.01 | 1.09 / 1.08 | 1.07 / 1.07 | +| Beta$(1,2)$ | 0.90 / 0.89 | 0.84 / 0.85 | 0.82 / 0.85 | 0.77 / 0.80 | +| Beta$(2,0.75)$ | 0.99 / 0.98 | 1.01 / 1.01 | 1.11 / 1.10 | 1.07 / 1.06 | +| Beta$(2,1)$ | 0.94 / 0.92 | 0.87 / 0.88 | 0.76 / 0.80 | 0.78 / 0.81 | +| Beta$(2,2)$ | 0.86 / 0.68 | 0.95 / 0.88 | 1.00 / 1.00 | 1.00 / 1.00 | +| Uniform | 0.94 / 0.96 | 0.86 / 0.91 | 0.76 / 0.81 | 0.72 / 0.78 | #### Two-sided, degree 1 | family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:| -| Beta$(0.75,0.75)$ | 0.91 / 0.91 | 0.87 / 0.88 | 0.94 / 0.95 | 0.97 / 0.97 | -| Beta$(0.75,2)$ | 0.88 / 0.87 | 0.89 / 0.90 | 0.96 / 0.97 | 0.98 / 0.98 | -| Beta$(1,2)$ | 0.81 / 0.76 | 0.72 / 0.74 | 0.73 / 0.76 | 0.69 / 0.73 | -| Beta$(2,0.75)$ | 0.89 / 0.88 | 0.88 / 0.88 | 0.95 / 0.96 | 0.98 / 0.98 | -| Beta$(2,1)$ | 0.86 / 0.82 | 0.74 / 0.76 | 0.70 / 0.75 | 0.71 / 0.74 | -| Beta$(2,2)$ | 0.91 / 0.73 | 0.96 / 0.90 | 1.00 / 1.00 | 1.00 / 1.00 | -| Uniform | 0.82 / 0.78 | 0.70 / 0.72 | 0.64 / 0.77 | 0.62 / 0.74 | +| Beta$(0.75,0.75)$ | 0.90 / 0.90 | 0.86 / 0.88 | 0.95 / 0.95 | 0.98 / 0.98 | +| Beta$(0.75,2)$ | 0.86 / 0.86 | 0.90 / 0.90 | 0.97 / 0.97 | 0.99 / 0.99 | +| Beta$(1,2)$ | 0.79 / 0.74 | 0.71 / 0.73 | 0.72 / 0.75 | 0.69 / 0.72 | +| Beta$(2,0.75)$ | 0.87 / 0.87 | 0.88 / 0.89 | 0.96 / 0.96 | 0.99 / 0.99 | +| Beta$(2,1)$ | 0.84 / 0.81 | 0.72 / 0.75 | 0.69 / 0.74 | 0.71 / 0.73 | +| Beta$(2,2)$ | 0.93 / 0.78 | 0.97 / 0.90 | 1.00 / 1.00 | 1.00 / 1.00 | +| Uniform | 0.79 / 0.76 | 0.68 / 0.70 | 0.62 / 0.76 | 0.61 / 0.73 | #### Two-sided, degree 2 | family | $n=25$ | $n=100$ | $n=1000$ | $n=2000$ | |---|---:|---:|---:|---:| -| Beta$(0.75,0.75)$ | 0.91 / 0.92 | 0.95 / 0.96 | 1.02 / 1.02 | 1.05 / 1.05 | -| Beta$(0.75,2)$ | 0.89 / 0.89 | 0.94 / 0.94 | 1.06 / 1.06 | 1.06 / 1.05 | -| Beta$(1,2)$ | 0.77 / 0.80 | 0.84 / 0.85 | 0.82 / 0.85 | 0.78 / 0.81 | -| Beta$(2,0.75)$ | 0.90 / 0.90 | 0.94 / 0.95 | 1.08 / 1.07 | 1.05 / 1.05 | -| Beta$(2,1)$ | 0.90 / 0.90 | 0.83 / 0.85 | 0.78 / 0.82 | 0.79 / 0.83 | -| Beta$(2,2)$ | 0.99 / 0.89 | 1.02 / 0.95 | 1.00 / 1.00 | 1.00 / 1.00 | -| Uniform | 0.87 / 0.87 | 0.86 / 0.90 | 0.82 / 0.86 | 0.79 / 0.83 | +| Beta$(0.75,0.75)$ | 0.90 / 0.91 | 0.94 / 0.95 | 1.04 / 1.04 | 1.07 / 1.07 | +| Beta$(0.75,2)$ | 0.87 / 0.88 | 0.95 / 0.96 | 1.09 / 1.08 | 1.08 / 1.07 | +| Beta$(1,2)$ | 0.74 / 0.77 | 0.82 / 0.83 | 0.81 / 0.83 | 0.77 / 0.79 | +| Beta$(2,0.75)$ | 0.89 / 0.89 | 0.95 / 0.96 | 1.11 / 1.10 | 1.07 / 1.07 | +| Beta$(2,1)$ | 0.89 / 0.89 | 0.80 / 0.82 | 0.76 / 0.80 | 0.77 / 0.81 | +| Beta$(2,2)$ | 1.04 / 0.96 | 1.04 / 0.96 | 1.00 / 1.00 | 1.00 / 1.00 | +| Uniform | 0.85 / 0.85 | 0.84 / 0.88 | 0.80 / 0.85 | 0.77 / 0.81 |
## Bias, variance, classification, and scale -The ISE gains are primarily a variance reduction, with some deliberate -small-sample boundary bias. Against pre-PR at scale 1, aggregate global -variance ratios are 0.27--0.53 one-sided for degree 0, 0.29--0.43 for degree 1, -and 0.04--0.12 for degree 2. Bounded ratios are 0.99--1.03, 0.86--0.90, and -0.89--1.00, respectively. This matches the visual goal: substantially calmer -one-sided endpoints and moderate smoothing on bounded support. +The repair primarily reduces variance, with deliberate boundary bias. Against +pre-PR at scale 1, aggregate global variance ratios are 0.38--0.62 one-sided +for degree 0, 0.39--0.56 for degree 1, and 0.20--0.24 for degree 2. Bounded +ratios are 0.96--0.98, 0.84--0.87, and 0.87--0.96, respectively. This matches +the visual goal: substantially calmer one-sided endpoints and moderate +smoothing on bounded support. Classifier behavior becomes appropriately conservative with sample size. For one-sided finite targets, selection rates at $n=100/2000$ are 58%/78% @@ -197,7 +197,7 @@ Gamma$(2)$. For Uniform, either endpoint is selected in 90%/98% and both in $n=100$ to 0% at $n\geq1000$. For Exponential samples at $n=100$, the 5%--95% range of the estimated value -at the endpoint is 0.56--1.44 when the expert is selected, compared with +at the endpoint is 0.64--1.34 when the expert is selected, compared with 0.01--49.6 when the classifier retains the raw bulk. Thus the expert delivers the intended visual stabilization when selected; remaining extreme endpoint values are primarily classifier false negatives. @@ -212,14 +212,14 @@ Median end-to-end R fit times for the default degree-2 estimator are below. | case | $n$ | pre-PR | candidate | slowdown | |---|---:|---:|---:|---:| -| one active endpoint | 100 | 0.48 ms | 0.81 ms | 1.70x | -| one active endpoint | 1,000 | 1.51 ms | 1.96 ms | 1.29x | -| one active endpoint | 10,000 | 12.43 ms | 13.57 ms | 1.09x | -| two active endpoints | 100 | 0.51 ms | 0.87 ms | 1.71x | -| two active endpoints | 1,000 | 1.45 ms | 1.85 ms | 1.27x | -| two active endpoints | 10,000 | 10.97 ms | 11.83 ms | 1.08x | -| one-sided fallback | 100 / 1,000 / 10,000 | -- | -- | 1.09x / 1.05x / 1.02x | -| two-sided fallback | 100 / 1,000 / 10,000 | -- | -- | 1.00x / 1.01x / 1.01x | +| one active endpoint | 100 | 0.48 ms | 0.79 ms | 1.66x | +| one active endpoint | 1,000 | 1.52 ms | 1.90 ms | 1.25x | +| one active endpoint | 10,000 | 12.47 ms | 13.23 ms | 1.06x | +| two active endpoints | 100 | 0.51 ms | 0.83 ms | 1.63x | +| two active endpoints | 1,000 | 1.46 ms | 1.77 ms | 1.22x | +| two active endpoints | 10,000 | 10.97 ms | 11.40 ms | 1.04x | +| one-sided fallback | 100 / 1,000 / 10,000 | -- | -- | 1.08x / 1.03x / 1.00x | +| two-sided fallback | 100 / 1,000 / 10,000 | -- | -- | 1.00x / 0.98x / 0.99x | ## Less common paths and numerical checks diff --git a/diagnostic/boundary-examples.png b/diagnostic/boundary-examples.png index 41094497a3eb6c24df2ae970be7a1fa3a154dd5e..281cf4288417c8eab38156dfc82a2732c9e4f03a 100644 GIT binary patch literal 169415 zcmb5W1yq%57d5(30Y#(*q@@J}M5IgDbR*KKl%#ZrA_~&dtso^OARv;0(uj12G}7I0 z*T(b59rwTEj=R6{odX#rZdsK79BvT;wNG4}TAz|Cg(l@q=rH z&wH8wkA+ZaSwO@1TD_M$3E^A}YI7t(E?an%RCx=EyuLsAn z>mNek48#A=Vt2;z-fD1A(B{U*!Afb@ zOMm}uQPagd&7v?W;cuqxv3-4gHJ3H^Z%H3yWsJOyz(xB9=b8mHYb#=AwaGpG> zm7Z;NvhMs3+dz?FSBZ5Lqhg8e3)A6^jg9=}*@G;{`40Z)Q}yAZXJ1{{Cn_BmQu!Ut 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