# `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_feature_selection_randomization_select`. R roxygen note (`methods_extra.R::randomization_select`): > Randomization test selector. > @param n_components Integer. Number of latent components. > @param n_permutations Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param randomization_seed Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param alpha Numeric in [0, 1]. Elastic-net / penalty mixing parameter. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export ### 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_randomization_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 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"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python 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) ``` ::: :::{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("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. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- randomization_select(X, Y, n_components, n_permutations = 100L, randomization_seed = 0L, alpha = 0.05) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.fit("randomization_select", X, y, "NumComponents", 4); yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("randomization_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`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`](../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 1.00181.1 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
::: :::{tab-item} 3 threads :sync: threads-3
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
::: :::{tab-item} 10 threads :sync: threads-10
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](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)