# `stability_select` — MC-UVE (Monte-Carlo coefficient stability) _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description Stability/MCUVE selection (§18 Phase 5c) From the `pls4all.sklearn.StabilitySelector` docstring: > MCUVE-style stability selector via Monte-Carlo subsampling. > **Registry note** — R `plsVarSel::mcuve_pls` Monte-Carlo UVE stability ranking with top-k truncation. Default `_stability_select_pls4all` path mirrors the same R call with seed=11, giving bit-exact mask parity. The C++ splitmix64 kernel is opt-in via `legacy=True`. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `top_k` | `int` | `None` | Number of features to retain. | | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `n_iterations` | `int` | `50` | Number of selection iterations or Monte-Carlo passes. | | `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. | | `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. | ## Explanations ### Bibliographic source Cai, W., Li, Y. & Shao, X. (2008). *A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra*. Chemometrics and Intelligent Laboratory Systems 90(2), 188–194. ### Mathematical principle MC-UVE evaluates the **stability** of each feature's PLS coefficient across Monte-Carlo subsamples of the calibration set: $\mathrm{stab}_j = |\bar{b}_j| / s(b_j)$, where $\bar{b}_j$ and $s(b_j)$ are the mean and standard deviation of $b_j$ across $B$ bootstrap fits. Features with high stability ratio are reliably predictive; those with low ratio are noise-driven and discarded. Conceptually a univariate analogue of stability selection (Meinshausen & Bühlmann 2010). The interaction with collinearity in the spectrum is benign: collinear features tend to share the contribution across bootstraps in a stable way, so their joint stability is high. Typical Monte-Carlo budget: $B = 50$–$200$ subsamples, each at 80 % of the calibration size. ### Implementation `n4m_feature_selection_stability_select`. Reference: R `plsVarSel`. R roxygen note (`methods_extra.R::stability_select`): > Stability selector (coefficient stability, MCUVE-style). > @param n_components Integer. Number of latent components. > @param top_k Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export MATLAB header (`bindings/matlab/+pls4all/stability_select.m`): ```text pls4all.stability_select Coefficient-stability selector (MCUVE-style). ``` ### Usage Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in `benchmarks.parity_timing.registry`. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN `pls` package (`plsr`, `pcr`, `mvr`) and for the `mdatools::pls(x, y, ...)` matrix idiom — those tabs appear only on the methods that have a meaningful equivalence. **pls4all bindings** ::::{tab-set} :class: pls4all-bindings :::{tab-item} C ABI · libn4m :sync: c :class-label: lang-c ```c /* C ABI — libn4m */ n4m_context_t* ctx = n4m_context_create(); n4m_config_t* cfg = n4m_config_create(); n4m_method_result_t* res = NULL; n4m_feature_selection_stability_select(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res); /* … read coefficients / mask / scores via */ /* n4m_method_result_get_double_matrix / vector / scalar … */ n4m_method_result_destroy(res); n4m_config_destroy(cfg); n4m_context_destroy(ctx); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python import pls4all from pls4all._methods import stability_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = stability_select_fit(ctx, cfg, X, y, n_components=4) # then: res.matrix("predictions"), res.matrix("coefficients"), # res.vector("mask"), res.scalar("intercept"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import StabilitySelector mdl = StabilitySelector(top_k, n_components=2, n_iterations=50, seed=0, n_folds=3) mdl.fit(X, y) y_hat = mdl.predict(X_test) ``` ::: :::{tab-item} R · pls4all_method() :sync: r-dispatcher :class-label: lang-r ```r library(pls4all) # Unified low-level dispatcher (May 2026 R cleanup): res <- pls4all_method("stability_select", X, y, n_components = 4L, params = list(top_k = 10L)) # res is a named list with MethodResult arrays/scalars. # selected_indices / top_k_intervals are 1-based. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- stability_select(X, Y, n_components, top_k = 10L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.stability_select(X, y, 4); % see header of bindings/matlab/+pls4all/stability_select.m for full % parameter surface: % res = stability_select(X, Y, n_components, top_k) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("stability_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.r_plsvarsel`** (R · r) — `plsVarSel` 0.10.0 · strict (rmse_rel ≤ 1e-06) — R `plsVarSel::mcuve_pls` Monte-Carlo UVE. Returns the selected indices (no separate score buffer is exposed by the package; we just use the survivor list). ::: ### Benchmarks Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). Only backends that implement this method are listed; libraries without the method are omitted. **Verdict**  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = pls4all binding agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆. **Reference gate**: strict — numeric equivalence (`rmse_rel_tol ≤ 1e-06`). Rows tagged with **📐** are the canonical parity references for this method (declared in [`parity_timing.registry`](../benchmarks/methodology.md)). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00690.4 ms
Python · pls4all
pls4all.python✓ J 1.001.7 s
pls4all.sklearn⇄ J 0.273.70 ms🏆
R · pls4all
pls4all.R⇄ J 0.2715.9 ms
pls4all.R.formula⇄ J 0.276.82 ms
pls4all.R.mdatools⇄ J 0.278.71 ms
pls4all.R.pls⇄ J 0.278.38 ms
R · external
📐ref.r_plsvarselsource492.8 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00727.7 ms
Python · pls4all
pls4all.python✓ J 1.00698.1 ms
pls4all.sklearn⇄ J 0.271.79 ms🏆
R · pls4all
pls4all.R⇄ J 0.276.01 ms
pls4all.R.formula⇄ J 0.275.91 ms
pls4all.R.mdatools⇄ J 0.276.92 ms
pls4all.R.pls⇄ J 0.278.89 ms
R · external
📐ref.r_plsvarselsource259.7 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00727.3 ms
Python · pls4all
pls4all.python✓ J 1.001.5 s
pls4all.sklearn⇄ J 0.271.92 ms🏆
R · pls4all
pls4all.R⇄ J 0.275.39 ms
pls4all.R.formula⇄ J 0.276.52 ms
pls4all.R.mdatools⇄ J 0.277.32 ms
pls4all.R.pls⇄ J 0.276.46 ms
R · external
📐ref.r_plsvarselsource230.9 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)