# `weighted_pls` — Sample-weighted PLS _Group_: **Robust / weighted** · _Registry tolerance_: `1e-08` ## 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_estimators_weighted_pls_fit` (in-sample only — no global coefficient export, since the weighted fit's $\bar{\mathbf{x}}, \bar{\mathbf{y}}$ depend on the weights). Python reference: sklearn `PLSRegression` on the prescaled matrices. R roxygen note (`sklearn_methods.R::weighted_pls`): > Sample-weighted PLS — formula entry point. > @param weights Numeric vector of length nrow(data) with sample weights. > @inheritParams pls > @export MATLAB header (`bindings/matlab/+pls4all/WeightedPlsRegression.m`): ```text pls4all.WeightedPlsRegression — sqrt(w)-prescaled SIMPLS. ``` ### 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_estimators_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); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python 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"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import WeightedPLSRegression mdl = WeightedPLSRegression(n_components=2) mdl.fit(X, y, sample_weight=sample_w) 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("weighted_pls", X, y, n_components = 4L) # 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 <- weighted_pls_fit(X, Y, n_components, sample_weights) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- weighted_pls(y ~ ., data = train, ncomp = 4L) yhat <- predict(fit, newdata = test) summary(fit) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab 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); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab ```matlab mdl = pls4all.fit("weighted_pls", X, y, "NumComponents", 4); yhat = predict(mdl, Xtest); ``` ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_scikit_learn`** (python · python) — `scikit-learn` 1.4.2 · strict (rmse_rel ≤ 1e-08) — 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`](../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-08`). 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
BackendParity200×50 (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
::: :::{tab-item} 3 threads :sync: threads-3
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
::: :::{tab-item} 10 threads :sync: threads-10
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](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)