# `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_feature_selection_st_select`. R roxygen note (`methods_extra.R::st_select`): > ST-PLS — score-threshold selector. > @param n_components Integer. Number of latent components. > @param thresholds Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param min_selected 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/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_feature_selection_st_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 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} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- st_select(X, Y, n_components, thresholds, min_selected = NULL) yhat <- pls4all_predict(res, X_test) ``` ::: :::{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  ·  ⇄ 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 1.00403.7 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
::: :::{tab-item} 3 threads :sync: threads-3
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
::: :::{tab-item} 10 threads :sync: threads-10
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](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)