# `st_select` — ST-PLS — Score Threshold selection
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
ST-PLS soft-thresholded sparse PLS (§18 Phase 5u)
From the `pls4all.sklearn.STSelector` docstring:
> ST-PLS — soft-thresholded sparse PLS selector.
> **Registry note** — R `plsVarSel::stpls` (Sæbø et al. 2008 ST-PLS, J. Chemom. 20, 54-62) with the shrink-ladder sweep (0.1, 0.3, 0.5, 0.7, 0.9) picking the most-shrunk model that still has >= min_selected non-zero coefs. Default `_st_select_pls4all` path mirrors the same R call with seed=11, giving bit-exact mask parity. The C++ absolute-threshold kernel is opt-in via `legacy=True`.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `thresholds` | `—` | `None` | Sequence of soft-threshold values to sweep; the most aggressive surviving subset is kept. |
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `min_selected` | `int | None` | `None` | Lower bound on the surviving feature count after thresholding. |
## Explanations
### Bibliographic source
Mehmood, T., Liland, K. H., Snipen, L. & Sæbø, S. (2012). *A review of variable selection methods in partial least squares regression*. Chemometrics and Intelligent Laboratory Systems 118, 62–69. https://doi.org/10.1016/j.chemolab.2012.07.010 — same review as `shaving_select`; §3.4 *Score-threshold methods* covers the deterministic-threshold family implemented here.
### Mathematical principle
Apply deterministic thresholds on the standardised coefficient (or VIP) scores: keep features whose absolute score exceeds the threshold $\tau$, with a minimum-retained fallback to avoid the empty selection. The benchmark scans a grid of thresholds and returns the subset with lowest CV-RMSE.
Conceptually similar to UVE but uses absolute thresholds rather than noise-baseline-relative ones. Less elegant but cheaper since no augmented noise matrix is needed.
### Implementation
`n4m_st_select`.
MATLAB header (`bindings/matlab/+pls4all/st_select.m`):
```text
pls4all.st_select Score-threshold selector (sweep over thresholds).
```
### 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_st_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 st_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = st_select_fit(ctx, cfg, X, y)
# 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 STSelector
mdl = STSelector(thresholds, n_components=2, min_selected=None)
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("st_select", X, y,
n_components = 2L)
# 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.st_select(X, y, 2);
% see header of bindings/matlab/+pls4all/st_select.m for full
% parameter surface:
% res = st_select(X, Y, n_components, thresholds, min_selected)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("st_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::stpls` (Sæbø et al. 2008) — soft-threshold PLS variable selection. We sweep the shrink parameter and pick the most aggressive shrinkage that still keeps ≥ `min_selected` features non-zero (mirrors pls4all's min-selected guard).
:::
### 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 | ≈ | 726.9 ms | 6.4 s🏆 | 7.5 s | 17.0 s | 532.2 ms | 480.7 ms | 6.9 s | 12.0 s | 51.5 s | 8.9 s🏆 | 46.1 s🏆 | 356.8 s | 21.4 s | 372.7 s |
pls4all.cpp.blas+omp | ≈ | 662.1 ms | 6.6 s | 7.6 s | 16.4 s | 548.3 ms | 449.5 ms | 6.8 s | 11.8 s🏆 | 52.1 s | 9.5 s | 53.1 s | 351.5 s🏆 | 21.1 s | 324.9 s🏆 |
pls4all.cpp.omp | ≈ | 757.5 ms | 6.6 s | 7.8 s | 16.1 s🏆 | 533.3 ms | 460.1 ms | 6.8 s🏆 | 13.0 s | 50.7 s🏆 | 9.3 s | 50.9 s | 371.4 s | 20.7 s🏆 | 367.9 s |
pls4all.cpp.ref | ≈ | 655.6 ms | 6.6 s | 7.5 s🏆 | 17.1 s | 537.0 ms | 459.0 ms | 7.1 s | 11.9 s | 51.9 s | 8.9 s | 52.8 s | 357.7 s | 21.3 s | 362.9 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 560.1 ms | — | — | — | 534.6 ms | 467.3 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 6.35 ms | — | — | — | 2.06 ms | 3.38 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 11.5 ms | — | — | — | 5.95 ms | 10.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 21.2 ms | — | — | — | 6.63 ms | 9.59 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 20.7 ms | — | — | — | 7.02 ms | 9.54 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 26.3 ms | — | — | — | 9.20 ms | 9.27 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 8.44 ms | — | — | — | 2.85 ms | 4.51 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 6.89 ms | — | — | — | 3.45 ms | 4.90 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 27.5 ms🏆 | — | — | — | 23.1 ms🏆 | 22.3 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 | — | — | — | — | 475.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 471.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 478.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 475.4 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 488.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.00 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.65 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.57 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.45 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.68 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.28 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.87 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 18.4 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 | — | — | — | — | 400.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 398.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 395.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 404.4 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 401.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.77 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.05 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.06 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 4.96 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.04 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.49 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.80 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 17.0 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)