mb_pls — Multi-block PLS (Westerhuis 1998)

Group: Multi-block / cross-modal · Registry tolerance: 2.0

Description

MB-PLS — Multi-block PLS (§17 Phase 4)

From the pls4all.sklearn.MBPLSRegression docstring:

Multi-block PLS (Westerhuis 1998).

Registry note — In-tree nirs4all.operators.models.sklearn.mbpls.MBPLS is the sanctioned external reference (the mbpls PyPI package is broken against sklearn 1.8). pls4all’s MB-PLS default now mirrors nirs4all NIPALS multi-block (standardize=False); the legacy block-balanced SIMPLS path is opt-in via cfg.scale_x=True.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

block_sizes

—

None

Sequence of contiguous block widths defining the X-block partition (columns of X).

n_blocks

int

3

registry benchmark cell value

Explanations

Bibliographic source

Westerhuis, J. A., Kourti, T. & MacGregor, J. F. (1998). Analysis of multiblock and hierarchical PCA and PLS models. Journal of Chemometrics 12(5), 301–321.

Mathematical principle

When predictors come from several distinct sources — NIR, MIR, Raman, process tags, lab assays — concatenating them into one wide matrix lets the block with the most variance dominate. Multi-block PLS instead block-scales each \(\mathbf{X}_b\) so blocks contribute proportionally to their information content rather than their dimensionality.

Formally, each block is centred and autoscaled, then scaled by \(1 / \sqrt{p_b}\) so its total variance is unit-normalised. PLS then runs on the concatenated \([\mathbf{X}_1, \ldots, \mathbf{X}_B]\) with optional per-block weights. Block-level importance statistics (block-VIP, block-RMSE) are recovered from the loadings by restriction to each block’s columns.

Compared to plain concatenation, MB-PLS gives interpretable per-block contributions and is the standard approach in process spectroscopy.

Implementation

n4m_mb_pls_fit — requires a block_sizes integer vector summing to \(p\). The C ABI materialises the intercept directly (no separate \(\bar{\mathbf{y}}\) key) because the block scaling changes the centring semantics. Reference: sanctioned git-pinned port nirs4all.operators.models.sklearn.mbpls.

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

pls4all.MbPlsRegression — Multi-block PLS.
 predict uses the stored intercept directly (coefficients are already
 in original X scale + intercept folds in y_mean - x_mean @ coef).

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_mb_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 mb_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = mb_pls_fit(ctx, cfg, X, y, n_components=3)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import MBPLSRegression
mdl = MBPLSRegression(n_components=2, block_sizes=None)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("mb_pls", X, y,
                      n_components = 3L, params = list(n_blocks = 3L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.mb_pls(X, y, 3);
% see header of bindings/matlab/+pls4all/mb_pls.m for full
% parameter surface:
%   res = mb_pls(X, Y, n_components, block_sizes)
yhat = predict(res, Xtest);

mdl  = pls4all.fit("mb_pls", X, y, "NumComponents", 3);
yhat = predict(mdl, Xtest);

Registry parity references 📐

  • 📐 nirs4all (python · python) — nirs4all in-tree · qualitative (rmse_rel ≤ 2e+00) — In-tree Python MB-PLS (sanctioned external reference). The mbpls PyPI package is broken against sklearn 1.8 (uses the deprecated force_all_finite kwarg). nirs4all’s implementation is a clean re-derivation of Westerhuis 1998.

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.

BackendParity200×60 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-162.37 ms🏆
Python · pls4all
pls4all.python✓ bind2.85 ms
pls4all.sklearn✓ 4e-152.59 ms
R · pls4all
pls4all.R✓ bind7.82 ms
pls4all.R.formula✓ bind10.9 ms
pls4all.R.mdatools✓ bind11.5 ms
pls4all.R.pls✓ bind10.2 ms
Python · external
📐nirs4allsource2.99 ms
BackendParity200×60 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-162.33 ms
Python · pls4all
pls4all.python✓ bind2.24 ms🏆
pls4all.sklearn✓ 4e-152.55 ms
R · pls4all
pls4all.R✓ bind7.24 ms
pls4all.R.formula✓ bind10.4 ms
pls4all.R.mdatools✓ bind9.38 ms
pls4all.R.pls✓ bind9.18 ms
Python · external
📐nirs4allsource7.12 ms
BackendParity200×60 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-1613.6 ms
Python · pls4all
pls4all.python✓ bind8.63 ms🏆
pls4all.sklearn✓ 4e-159.61 ms
R · pls4all
pls4all.R✓ bind30.4 ms
pls4all.R.formula✓ bind46.5 ms
pls4all.R.mdatools✓ bind48.5 ms
pls4all.R.pls✓ bind41.0 ms
Python · external
📐nirs4allsource9.70 ms

See also: benchmark overview · methods index · interactive dashboard