bagging_pls — Bagging PLS

Group: Ensemble · Registry tolerance: 1e-06

Description

Bagging PLS (§20)

From the pls4all.sklearn.BaggingPLSRegression docstring:

Bagged PLS (Breiman 1996).

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

seed

int

0

Random seed for reproducible sampling/initialization.

Explanations

Bibliographic source

Breiman, L. (1996). Bagging predictors. Machine Learning 24(2), 123–140. — adapted for PLS by various chemometric authors.

Mathematical principle

Bootstrap aggregating draws \(B\) bootstrap samples \(\{(\mathbf{X}^{(b)}, \mathbf{y}^{(b)})\}_{b=1}^{B}\) from the calibration set (sampling with replacement, \(n\) rows each), fits a PLS model on each, and averages the predictions: \(\hat{y}_{\mathrm{bag}}(\mathbf{x}) = \frac{1}{B}\sum_b \hat{y}^{(b)}(\mathbf{x})\).

PLS is a high-bias / low-variance learner, so bagging rarely beats a single well-tuned PLS in pure RMSE. Its real value is inferential: the bootstrap distribution of coefficients gives non-parametric standard errors and confidence intervals that are otherwise inaccessible. The per-bag \(\mathbf{B}^{(b)}\) matrices form an empirical distribution from which posterior intervals on each feature’s contribution can be read off.

Computational cost: \(B\) times a single fit, embarrassingly parallel. Use \(B \in [50, 500]\) depending on how stable the CIs need to be.

Implementation

n4m_bagging_pls_fit. Reference: CRAN enpls 6.1.1.

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_bagging_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 bagging_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = bagging_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 BaggingPLSRegression
mdl = BaggingPLSRegression(n_components=2, n_estimators=50, 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("bagging_pls", X, y,
                      n_components = 4L, params = list(n_estimators = 10L, seed = 42L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.bagging_pls(X, y, 4);
% see header of bindings/matlab/+pls4all/bagging_pls.m for full
% parameter surface:
%   res = bagging_pls(X, Y, n_components, n_estimators, seed)
yhat = predict(res, Xtest);

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

Registry parity references 📐

  • 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.8.0 · strict (rmse_rel ≤ 1e-06) — sklearn BaggingRegressor(PLSRegression(scale=False), bootstrap=True, max_samples=1.0). pls4all wraps the same sklearn objects, giving bit-for-bit 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✓ ref9.82 ms
Python · pls4all
pls4all.python✓ bind9.30 ms
pls4all.sklearn⇄ +2e-011.69 ms🏆
R · pls4all
pls4all.R⇄ +2e-014.62 ms
pls4all.R.formula⇄ +2e-016.41 ms
pls4all.R.mdatools⇄ +2e-015.11 ms
pls4all.R.pls⇄ +2e-014.93 ms
Python · external
📐ref.python_scikit_learnsource11.1 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref21.7 ms
Python · pls4all
pls4all.python✓ bind60.8 ms
pls4all.sklearn⇄ +2e-0111.4 ms🏆
R · pls4all
pls4all.R⇄ +2e-0125.2 ms
pls4all.R.formula⇄ +2e-0140.6 ms
pls4all.R.mdatools⇄ +2e-0146.3 ms
pls4all.R.pls⇄ +2e-0145.0 ms
Python · external
📐ref.python_scikit_learnsource56.1 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref27.8 ms
Python · pls4all
pls4all.python✓ bind12.7 ms
pls4all.sklearn⇄ +2e-012.54 ms🏆
R · pls4all
pls4all.R⇄ +2e-015.73 ms
pls4all.R.formula⇄ +2e-016.42 ms
pls4all.R.mdatools⇄ +2e-017.63 ms
pls4all.R.pls⇄ +2e-017.41 ms
Python · external
📐ref.python_scikit_learnsource14.2 ms

See also: benchmark overview · methods index · interactive dashboard