random_subspace_pls — Random-subspace PLS

Group: Ensemble · Registry tolerance: 1e-06

Description

Random-subspace PLS (§20)

From the pls4all.sklearn.RandomSubspacePLSRegression docstring:

Random-subspace PLS — Ho 1998.

Registry note — sklearn BaggingRegressor(PLSRegression(scale=False), max_features=k, bootstrap=False, bootstrap_features=False, max_samples=1.0). pls4all’s default now mirrors this convention exactly (same RNG, feature-subset order, and prediction averaging), so the gate is bit-for-bit. The legacy single-pass C++ kernel (splitmix feature shuffle + coefficient averaging) is opt-in via legacy=True.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

n_estimators

int

50

Number of base PLS sub-models in the ensemble.

features_per_subspace

int

10

Number of features randomly drawn per random-subspace base learner.

seed

int

0

Random seed for reproducible sampling/initialization.

Explanations

Bibliographic source

Ho, T. K. (1998). The random subspace method for constructing decision forests. IEEE TPAMI 20(8), 832–844. — adapted for PLS regressors.

Mathematical principle

Each ensemble member fits PLS on a random subset of \(m \ll p\) features. Compared to bagging (which randomises rows), random subspaces randomise columns, which is a much stronger variance-reduction mechanism for high-dimensional collinear data like NIR spectra: different subsets pick up different bands of the spectrum, and averaging across them smooths out band-specific noise.

Variance per member is higher than a full-feature PLS (less information per fit), but the ensemble average outperforms a single fit when the underlying truth is spread across many weakly-correlated features. Choosing \(m \approx \sqrt{p}\) is a Breiman-style default; for spectra a more informed choice respects band widths.

Note that prediction on a new sample requires evaluating every member on its own subset of features, so the feature-index map must be stored per member.

Implementation

n4m_random_subspace_pls_fit.

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_random_subspace_pls_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 random_subspace_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = random_subspace_pls_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 RandomSubspacePLSRegression
mdl = RandomSubspacePLSRegression(n_components=2, n_estimators=50, features_per_subspace=10, seed=0)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("random_subspace_pls", X, y,
                      n_components = 4L, params = list(n_estimators = 10L, features_per_subspace = 20L, seed = 42L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

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

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

Registry parity references 📐

  • 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.8.0 · strict (rmse_rel ≤ 1e-06) — sklearn BaggingRegressor(PLSRegression(), max_features=…, bootstrap=False). Random feature subspaces with full sample rows, matching pls4all’s sampling shape. RNG differs from pls4all; qualitative parity.

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.

BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref13.5 ms
Python · pls4all
pls4all.python✓ bind13.2 ms
pls4all.sklearn⇄ +9e-011.54 ms🏆
R · pls4all
pls4all.R⇄ +9e-015.11 ms
pls4all.R.formula⇄ +9e-015.82 ms
pls4all.R.mdatools⇄ +9e-016.22 ms
pls4all.R.pls⇄ +9e-015.56 ms
Python · external
📐ref.python_scikit_learnsource13.0 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref12.1 ms
Python · pls4all
pls4all.python✓ bind13.6 ms
pls4all.sklearn⇄ +9e-012.67 ms🏆
R · pls4all
pls4all.R⇄ +9e-014.41 ms
pls4all.R.formula⇄ +9e-015.82 ms
pls4all.R.mdatools⇄ +9e-016.51 ms
pls4all.R.pls⇄ +9e-016.01 ms
Python · external
📐ref.python_scikit_learnsource10.4 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref9.97 ms
Python · pls4all
pls4all.python✓ bind11.1 ms
pls4all.sklearn⇄ +9e-011.65 ms🏆
R · pls4all
pls4all.R⇄ +9e-014.27 ms
pls4all.R.formula⇄ +9e-015.12 ms
pls4all.R.mdatools⇄ +9e-017.43 ms
pls4all.R.pls⇄ +9e-015.33 ms
Python · external
📐ref.python_scikit_learnsource26.1 ms

See also: benchmark overview · methods index · interactive dashboard