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

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):

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

/* 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);

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"), …

from pls4all.sklearn import STSelector
mdl = STSelector(thresholds, n_components=2, min_selected=None)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

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.

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);

No idiomatic classdef wrapper — invoke pls4all.fit("st_select", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 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. 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). 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.

BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00403.7 ms
Python · pls4all
pls4all.python✓ J 1.00418.3 ms
pls4all.sklearn⇄ J 0.571.82 ms🏆
R · pls4all
pls4all.R⇄ J 0.576.05 ms
pls4all.R.formula⇄ J 0.575.27 ms
pls4all.R.mdatools⇄ J 0.575.45 ms
pls4all.R.pls⇄ J 0.575.46 ms
R · external
📐ref.r_plsvarselsource17.8 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00399.6 ms
Python · pls4all
pls4all.python✓ J 1.00400.5 ms
pls4all.sklearn⇄ J 0.571.95 ms🏆
R · pls4all
pls4all.R⇄ J 0.574.89 ms
pls4all.R.formula⇄ J 0.576.39 ms
pls4all.R.mdatools⇄ J 0.578.78 ms
pls4all.R.pls⇄ J 0.575.32 ms
R · external
📐ref.r_plsvarselsource17.5 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00429.2 ms
Python · pls4all
pls4all.python✓ J 1.00435.3 ms
pls4all.sklearn⇄ J 0.571.78 ms🏆
R · pls4all
pls4all.R⇄ J 0.574.31 ms
pls4all.R.formula⇄ J 0.576.27 ms
pls4all.R.mdatools⇄ J 0.576.77 ms
pls4all.R.pls⇄ J 0.575.49 ms
R · external
📐ref.r_plsvarselsource19.4 ms

See also: benchmark overview · methods index · interactive dashboard