weighted_pls — Sample-weighted PLS

Group: Robust / weighted · Registry tolerance: 0.1

Description

Sample-weighted PLS (sqrt(w)-prescaled NIPALS)

From the pls4all.sklearn.WeightedPLSRegression docstring:

Sample-weighted PLS (sqrt(w)-prescaled SIMPLS).

Registry note — sklearn PLSRegression on the sqrt(w)-prescaled centered data is mathematically equivalent to weighted PLS. Both sides default to NIPALS, matching to ~1e-12. SIMPLS is still available as an opt-in via cfg.solver = pls4all.Solver.SIMPLS.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

Explanations

Bibliographic source

Martens, H. & Næs, T. (1989). Multivariate Calibration. Wiley. §4.5 ‘Weighted regression for non-i.i.d. errors’.

Mathematical principle

When the residual variance is not constant across samples — typical when calibration spectra are aggregated across instruments, sites or operators — a weighted least squares fit can dramatically improve generalisation. Weighted PLS prescales centred rows by \(\sqrt{w_i}\) before extracting the SIMPLS components: \(\tilde{\mathbf{X}} = \operatorname{diag}(\sqrt{w})\,\mathbf{X}_c, \quad \tilde{\mathbf{Y}} = \operatorname{diag}(\sqrt{w})\,\mathbf{Y}_c\), then runs vanilla SIMPLS on \((\tilde{\mathbf{X}}, \tilde{\mathbf{Y}})\).

Weights \(w_i > 0\) encode any known per-sample reliability: inverse residual variance from a previous fit, instrument noise estimates, sample replicate counts. The weighted fit is mathematically equivalent to running standard PLS on a duplicated dataset where each row appears \(w_i\) times.

This is a building block for robust PLS (IRLS over a weighted fit) and for incorporating known measurement noise into the calibration.

Implementation

n4m_weighted_pls_fit exports coefficients, predictions, x_mean and y_mean; the centering vectors are weight-dependent, so replaying predictions on new samples requires reconstructing the fit intercept as y_mean - x_mean @ coefficients. Python reference: sklearn PLSRegression on the prescaled matrices.

MATLAB header (bindings/matlab/+pls4all/WeightedPlsRegression.m):

pls4all.WeightedPlsRegression — sqrt(w)-prescaled SIMPLS.

Usage

Direct n4m Python helper:

import numpy as np
import n4m

sample_w = np.ones(X.shape[0])
res = n4m.weighted_pls(X, y, sample_weights=sample_w, n_components=4)
y_hat = res["predictions"]
coef = res["coefficients"]

The n4m.sklearn.NativeWeightedPLSRegressor wrapper replays predictions from the returned coefficients plus reconstructed intercept. Use sample_weights as an estimator parameter when training-row weights are part of the fit contract.

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

from pls4all.sklearn import WeightedPLSRegression
mdl = WeightedPLSRegression(n_components=2)
mdl.fit(X, y, sample_weight=sample_w)
y_hat = mdl.predict(X_test)

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

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

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

Registry parity references 📐

  • 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.4.2 · qualitative (rmse_rel ≤ 1e-01) — Weighted PLS computed via sklearn PLSRegression on the sqrt(w)-prescaled centered (X, Y). sklearn is the external PLS engine; the row-scaling is a standard preconditioning step that is mathematically equivalent to weighted PLS.

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-08).

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.

BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 4e-151.93 ms
Python · pls4all
pls4all.python✓ bind1.77 ms🏆
pls4all.sklearn✓ 3e-131.92 ms
R · pls4all
pls4all.R✓ 3e-134.57 ms
pls4all.R.formula✓ 3e-135.88 ms
pls4all.R.mdatools✓ 3e-135.95 ms
pls4all.R.pls✓ 3e-135.23 ms
Python · external
📐ref.python_scikit_learnsource2.12 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 4e-151.81 ms🏆
Python · pls4all
pls4all.python✓ bind1.87 ms
pls4all.sklearn✓ 3e-131.84 ms
R · pls4all
pls4all.R✓ 3e-135.06 ms
pls4all.R.formula✓ 3e-135.37 ms
pls4all.R.mdatools✓ 3e-135.52 ms
pls4all.R.pls✓ 3e-136.02 ms
Python · external
📐ref.python_scikit_learnsource2.23 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 4e-151.82 ms🏆
Python · pls4all
pls4all.python✓ bind1.91 ms
pls4all.sklearn✓ 3e-131.91 ms
R · pls4all
pls4all.R✓ 3e-134.82 ms
pls4all.R.formula✓ 3e-135.68 ms
pls4all.R.mdatools✓ 3e-135.35 ms
pls4all.R.pls✓ 3e-136.10 ms
Python · external
📐ref.python_scikit_learnsource2.18 ms

See also: benchmark overview · methods index · interactive dashboard