# `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_stability_select`. Reference: R `plsVarSel`.
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_stability_select_fit(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} 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 · ✗ 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
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ≈ | 944.9 ms | 889.0 ms | 1.9 s🏆 | 7.9 s | 715.6 ms | 854.8 ms | 2.7 s🏆 | 34.8 s🏆 | 173.4 s | 60.6 s | 877.2 s | — | — | — |
pls4all.cpp.blas+omp | ≈ | 582.5 ms | 880.5 ms | 2.0 s | 7.7 s🏆 | 702.2 ms | 810.3 ms | 2.8 s | 35.4 s | 173.0 s | 61.4 s | 880.4 s | — | — | — |
pls4all.cpp.omp | ≈ | 912.5 ms | 871.3 ms🏆 | 2.0 s | 7.9 s | 701.2 ms | 816.0 ms | 2.8 s | 35.2 s | 171.6 s🏆 | 61.7 s | 881.1 s | — | — | — |
pls4all.cpp.ref | ≈ | 537.1 ms | 887.6 ms | 1.9 s | 8.3 s | 718.5 ms | 899.3 ms | 2.7 s | 35.1 s | 176.6 s | 60.5 s🏆 | 873.2 s🏆 | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 600.3 ms | — | — | — | 712.8 ms | 814.6 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 4.70 ms | — | — | — | 2.05 ms | 5.89 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 13.4 ms | — | — | — | 5.43 ms | 13.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 20.9 ms | — | — | — | 8.16 ms | 13.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 18.9 ms | — | — | — | 6.48 ms | 9.19 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 19.4 ms | — | — | — | 6.73 ms | 11.0 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.80 ms | — | — | — | 2.81 ms | 4.69 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 5.28 ms | — | — | — | 3.09 ms | 5.14 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 101.8 ms🏆 | — | — | — | 243.0 ms🏆 | 387.5 ms🏆 | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 639.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 640.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 640.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 642.9 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 652.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.01 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.24 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.07 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 7.08 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 7.01 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.67 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.07 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 215.1 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 547.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 548.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 554.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 551.0 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 549.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.63 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 3.77 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 4.55 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 4.60 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 4.66 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.40 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.69 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 206.0 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)