# `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
| Backend | Parity | 200×40 (ms) |
| C++ native · libn4m |
pls4all.cpp.blas+omp | ✓ J 1.00 | 690.4 ms |
| Python · pls4all |
pls4all.python | ✓ J 1.00 | 1.7 s |
pls4all.sklearn | ⇄ J 0.27 | 3.70 ms🏆 |
| R · pls4all |
pls4all.R | ⇄ J 0.27 | 15.9 ms |
pls4all.R.formula | ⇄ J 0.27 | 6.82 ms |
pls4all.R.mdatools | ⇄ J 0.27 | 8.71 ms |
pls4all.R.pls | ⇄ J 0.27 | 8.38 ms |
| R · external |
📐ref.r_plsvarsel | source | 492.8 ms |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 200×40 (ms) |
| C++ native · libn4m |
pls4all.cpp.blas+omp | ✓ J 1.00 | 727.7 ms |
| Python · pls4all |
pls4all.python | ✓ J 1.00 | 698.1 ms |
pls4all.sklearn | ⇄ J 0.27 | 1.79 ms🏆 |
| R · pls4all |
pls4all.R | ⇄ J 0.27 | 6.01 ms |
pls4all.R.formula | ⇄ J 0.27 | 5.91 ms |
pls4all.R.mdatools | ⇄ J 0.27 | 6.92 ms |
pls4all.R.pls | ⇄ J 0.27 | 8.89 ms |
| R · external |
📐ref.r_plsvarsel | source | 259.7 ms |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 200×40 (ms) |
| C++ native · libn4m |
pls4all.cpp.blas+omp | ✓ J 1.00 | 727.3 ms |
| Python · pls4all |
pls4all.python | ✓ J 1.00 | 1.5 s |
pls4all.sklearn | ⇄ J 0.27 | 1.92 ms🏆 |
| R · pls4all |
pls4all.R | ⇄ J 0.27 | 5.39 ms |
pls4all.R.formula | ⇄ J 0.27 | 6.52 ms |
pls4all.R.mdatools | ⇄ J 0.27 | 7.32 ms |
pls4all.R.pls | ⇄ J 0.27 | 6.46 ms |
| R · external |
📐ref.r_plsvarsel | source | 230.9 ms |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)