randomization_select — Randomisation test (Y-permutation)

Group: Variable selector · Registry tolerance: 1e-06

Description

Randomization-test selector (§18 Phase 5o)

From the pls4all.sklearn.RandomizationSelector docstring:

Randomization-test PLS selector (Y-permutation p-values).

Registry note — Base R: SIMPLS coefs vs permuted-Y null distribution. Default _randomization_select_pls4all path mirrors the same base-R permutation test with seed=randomization_seed, giving bit-exact mask parity. The C++ splitmix64 kernel is opt-in via legacy=True.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

n_permutations

int

200

Number of Y-permutations used to build the null distribution.

randomization_seed

int

0

Seed for the permutation generator.

alpha

float

0.05

Significance level for the permutation-based variable retention test.

Explanations

Bibliographic source

Westad, F. & Martens, H. (2000). Variable selection in near infrared spectroscopy based on significance testing in partial least squares regression. JNIRS 8(2), 117–124.

Mathematical principle

Compute the observed PLS coefficient magnitudes \(|b_j^{\mathrm{obs}}|\), then permute \(\mathbf{y}\) \(M\) times, refit PLS each time, and collect \(|b_j^{(m)}|\). The empirical p-value of feature \(j\) is \(p_j = \frac{1 + \#\{m : |b_j^{(m)}| \ge |b_j^{\mathrm{obs}}|\}}{1 + M}\). Retain features with \(p_j < \alpha\).

Y-permutation is the gold standard for null-calibrated significance testing in PLS — no distributional assumptions, no asymptotic approximations. Cost is \(M\)× a fit but trivially parallelisable.

Critically, Y-permutation tests the joint hypothesis ‘feature \(j\) contributes to \(y\)’; multiple-testing correction (Benjamini-Hochberg) is recommended for \(p \gg 100\).

Implementation

n4m_randomization_select.

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_randomization_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 randomization_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = randomization_select_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import RandomizationSelector
mdl = RandomizationSelector(n_components=2, n_permutations=200, randomization_seed=0, alpha=0.05)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("randomization_select", X, y,
                      n_components = 4L, params = list(n_permutations = 50L, alpha = 0.05, randomization_seed = 11L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res  = pls4all.fit("randomization_select", X, y, "NumComponents", 4);
yhat = predict(res, Xtest);

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

Registry parity references 📐

  • 📐 ref.r_pls_stats (R · r) — pls+stats R 4.3.3 · strict (rmse_rel ≤ 1e-06) — Base R: SIMPLS coefficients vs permuted-Y null distribution. Selects features with empirical p-value < alpha. Same idea as pls4all’s randomization_test selector.

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 1.00181.1 ms
Python · pls4all
pls4all.python✓ J 1.00182.5 ms
pls4all.sklearn✓ J 1.002.67 ms🏆
R · pls4all
pls4all.R✓ J 1.006.34 ms
pls4all.R.formula✓ J 1.005.94 ms
pls4all.R.mdatools✓ J 1.006.29 ms
pls4all.R.pls✓ J 1.006.80 ms
R · external
📐ref.r_pls_statssource54.5 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00187.4 ms
Python · pls4all
pls4all.python✓ J 1.00190.6 ms
pls4all.sklearn✓ J 1.002.80 ms🏆
R · pls4all
pls4all.R✓ J 1.006.12 ms
pls4all.R.formula✓ J 1.006.58 ms
pls4all.R.mdatools✓ J 1.006.46 ms
pls4all.R.pls✓ J 1.006.95 ms
R · external
📐ref.r_pls_statssource57.0 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00222.2 ms
Python · pls4all
pls4all.python✓ J 1.00218.8 ms
pls4all.sklearn✓ J 1.002.78 ms🏆
R · pls4all
pls4all.R✓ J 1.006.42 ms
pls4all.R.formula✓ J 1.006.83 ms
pls4all.R.mdatools✓ J 1.007.18 ms
pls4all.R.pls✓ J 1.007.31 ms
R · external
📐ref.r_pls_statssource56.8 ms

See also: benchmark overview · methods index · interactive dashboard