recursive_pls — Recursive (moving-window) PLS

Group: Core PLS · Registry tolerance: 0.1

Description

Recursive (moving-window) PLS

From the pls4all.sklearn.RecursivePLSRegression docstring:

Moving-window recursive PLS.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

window_size

int

50

Length of the moving window for recursive / interval-random-frog models.

Explanations

Bibliographic source

Helland, K., Berntsen, H. E., Borgen, O. S. & Martens, H. (1992). Recursive algorithm for partial least squares regression. Chemometrics and Intelligent Laboratory Systems 14(1–3), 129–137.

Mathematical principle

Process-analytical instruments produce streams of spectra under drifting conditions (changing humidity, instrument warm-up, fouling). Recursive PLS maintains a fitted model that adapts as new samples arrive by re-fitting on a sliding window of the most recent \(w\) samples.

At time step \(t\), the model is fit on \(\{(\mathbf{x}_{t-w+1}, y_{t-w+1}), \ldots, (\mathbf{x}_t, y_t)\}\) and applied to incoming \(\mathbf{x}_{t+1}\). Computational cost is \(O(wpk)\) per step. The window width \(w\) controls a stability/adaptability trade-off: short windows track drift aggressively but are noisier; long windows are stable but lag.

More sophisticated recursive variants (Qin 1998) use exponential forgetting factors instead of a hard window. pls4all’s variant uses the hard-window form for deterministic parity with R pls rolling refits.

Implementation

n4m_recursive_pls_run (returns predictions only — no global coefficient export, since the model changes per step). The Python sklearn wrapper is an in-sample-only estimator.

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

pls4all.RecursivePlsRegression  Moving-window recursive PLS.
 In-sample only: result holds in-window predictions; no global coefficient
 matrix. `predict(X)` returns the stored predictions for the training X
 (length-preserved; warmup samples are 0).

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

from pls4all.sklearn import RecursivePLSRegression
mdl = RecursivePLSRegression(n_components=2, window_size=50)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("recursive_pls", X, y,
                      n_components = 3L, params = list(window_size = 60L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

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

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

Registry parity references 📐

  • 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.4.2 · qualitative (rmse_rel ≤ 1e-01) — Moving-window refit using sklearn PLSRegression (NIPALS).

  • 📐 ref.r_pls (R · r) — pls 2.8.5 · qualitative (rmse_rel ≤ 1e-01) — Moving-window refit using R pls::plsr (SIMPLS by default).

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 9e-162.92 ms
Python · pls4all
pls4all.python✓ bind2.79 ms🏆
pls4all.sklearn✓ bind3.10 ms
R · pls4all
pls4all.R✓ 4e-155.74 ms
pls4all.R.formula✓ 4e-156.55 ms
pls4all.R.mdatools✓ 4e-156.99 ms
pls4all.R.pls✓ 4e-157.36 ms
Python · external
📐ref.python_scikit_learnsource48.1 ms
R · external
📐ref.r_pls⇄ +4e-15141.6 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 9e-162.87 ms🏆
Python · pls4all
pls4all.python✓ bind2.94 ms
pls4all.sklearn✓ bind3.11 ms
R · pls4all
pls4all.R✓ 4e-155.97 ms
pls4all.R.formula✓ 4e-156.97 ms
pls4all.R.mdatools✓ 4e-157.91 ms
pls4all.R.pls✓ 4e-156.92 ms
Python · external
📐ref.python_scikit_learnsource46.3 ms
R · external
📐ref.r_pls⇄ +4e-15144.8 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 9e-162.95 ms🏆
Python · pls4all
pls4all.python✓ bind3.02 ms
pls4all.sklearn✓ bind3.06 ms
R · pls4all
pls4all.R✓ 4e-155.98 ms
pls4all.R.formula✓ 4e-157.42 ms
pls4all.R.mdatools✓ 4e-156.94 ms
pls4all.R.pls✓ 4e-157.32 ms
Python · external
📐ref.python_scikit_learnsource48.7 ms
R · external
📐ref.r_pls⇄ +4e-15147.3 ms

See also: benchmark overview · methods index · interactive dashboard