# `pls_logistic` — PLS-logistic regression _Group_: **Classification & GLM** · _Registry tolerance_: `1e-08` ## Description PLS-Logistic — Logistic regression on PLS scores From the `pls4all.sklearn.PLSLogisticClassifier` docstring: > PLS-Logistic: PLS scores fed into multinomial softmax IRLS. > **Registry note** — sklearn `PLSRegression -> LogisticRegression` pipeline vs pls4all's single-pass PLS + softmax IRLS. Latent decompositions differ; parity is qualitative. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `n_classes` | `int` | `3` | registry benchmark cell value | ## Explanations ### Bibliographic source Bastien, P., Esposito Vinzi, V. & Tenenhaus, M. (2005). *PLS generalised linear regression*. Computational Statistics & Data Analysis 48(1), 17–46. ### Mathematical principle Iteratively-reweighted-least-squares PLS with a logit link function. At each iteration the current predictor is converted to a working response via $z_i = \eta_i + (y_i - p_i) / (p_i(1 - p_i))$ where $p_i = 1/(1 + e^{-\eta_i})$, a PLS fit is run on $(\mathbf{X}, \mathbf{z})$ with weights $p_i(1 - p_i)$, and the linear predictor is updated. This is the natural extension of PLS to binary / multinomial classification when class probabilities (rather than hard labels or class scores) are needed, and it generalises smoothly to GLM families beyond Bernoulli (Poisson — see `pls_glm`). The multinomial case extends to $K$ classes via a softmax link. Convergence is typically reached in 5–10 IRLS iterations. The Bastien et al. variant is closely related to Marx 1996's *Iteratively Reweighted PLS* but differs in the deflation convention. ### Implementation `n4m_estimators_pls_logistic_fit` (in-sample only). Reference: R `plsRglm 1.7.0`. R roxygen note (`methods_extra.R::pls_logistic_fit`): > Multinomial logistic regression on PLS scores. > @param y_labels Integer vector. Class labels. > @param n_components Integer. Number of latent components. > @param n_classes Integer >= 2. Number of class labels. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @export MATLAB header (`bindings/matlab/+pls4all/pls_logistic.m`): ```text pls4all.pls_logistic Multinomial logistic regression on PLS scores. ``` ### 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_pls_logistic_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 pls_logistic_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = pls_logistic_fit(ctx, cfg, X, y, n_components=3, y_labels=y_labels) # 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 PLSLogisticClassifier mdl = PLSLogisticClassifier(n_components=2) mdl.fit(X, y) 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("pls_logistic", X, y, n_components = 3L, params = list(n_classes = 3L)) # 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 <- pls_logistic_fit(X, y_labels, n_components, n_classes = NULL) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.pls_logistic(X, y, 3); % see header of bindings/matlab/+pls4all/pls_logistic.m for full % parameter surface: % res = pls_logistic(X, y_labels, n_components, n_classes) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("pls_logistic", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_scikit_learn`** (python · python) — `scikit-learn` 1.8.0 · strict (rmse_rel ≤ 1e-08) — sklearn `PLSRegression -> LogisticRegression` pipeline. pls4all's PLS-Logistic does a single PLS + softmax IRLS in C; sklearn fits PLS on one-hot Y, then a multinomial LogisticRegression on the scores. Both are valid PLS-logistic pipelines but the latent decompositions differ; parity is on the decision-score shape. ::: ### 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
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-163.14 ms🏆
Python · pls4all
pls4all.python✓ bind3.34 ms
Python · external
📐ref.python_scikit_learnsource3.44 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-163.20 ms🏆
Python · pls4all
pls4all.python✓ bind3.81 ms
Python · external
📐ref.python_scikit_learnsource23.2 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-164.74 ms
Python · pls4all
pls4all.python✓ bind4.36 ms🏆
Python · external
📐ref.python_scikit_learnsource5.41 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)