# `pls_logistic` — PLS-logistic regression
_Group_: **Classification & GLM** · _Registry tolerance_: `5.0`
## 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_pls_logistic_fit` (in-sample only). Reference: R `plsRglm 1.7.0`.
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_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} 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 · qualitative (rmse_rel ≤ 5e+00) — 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 · ✗ divergent · ⚠ error · — not run. The fastest backend per column is marked 🏆.
**Reference gate**: qualitative — shape/smoke comparison only. The external library and pls4all do not produce numerically equivalent output for this method (see the MethodSpec notes); the `rmse_rel_tol ≤ 5e+00` budget is set wide on purpose. Treat ~ shape as *“we ran both, both finished”*, not as numerical agreement.
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
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ≈ +7e-16 | 5.59 ms | 5.33 ms | 17.9 ms | 66.9 ms | 4.26 ms | 4.85 ms | 7.96 ms🏆 | 70.2 ms | 337.1 ms | 37.4 ms | 333.2 ms🏆 | 1.7 s | 130.8 ms | 1.3 s |
pls4all.cpp.blas+omp | ≈ +7e-16 | 5.11 ms | 3.78 ms🏆 | 15.6 ms | 66.1 ms | 4.11 ms | 4.92 ms | 9.37 ms | 70.1 ms | 324.6 ms🏆 | 37.5 ms | 351.5 ms | 1.7 s | 133.8 ms | 1.3 s |
pls4all.cpp.omp | ≈ +8e-16 | 4.36 ms🏆 | 4.33 ms | 16.3 ms | 68.3 ms | 2.77 ms | 4.23 ms | 9.91 ms | 70.4 ms | 343.1 ms | 36.3 ms | 333.3 ms | 1.7 s | 126.3 ms🏆 | 1.3 s |
pls4all.cpp.ref | ≈ +8e-16 | 5.44 ms | 4.22 ms | 15.3 ms🏆 | 64.0 ms🏆 | 2.72 ms🏆 | 3.64 ms🏆 | 8.90 ms | 67.8 ms🏆 | 339.6 ms | 34.3 ms🏆 | 336.7 ms | 1.7 s🏆 | 140.6 ms | 1.3 s🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 4.75 ms | — | — | — | 2.94 ms | 5.35 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+01 | 3.13 ms | — | — | — | 2.39 ms | 3.74 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+01 | 14.8 ms | — | — | — | 6.28 ms | 13.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+01 | 21.9 ms | — | — | — | 6.67 ms | 13.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+01 | 21.8 ms | — | — | — | 7.11 ms | 10.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+01 | 24.2 ms | — | — | — | 6.82 ms | 10.4 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+01 | 6.21 ms | — | — | — | 2.90 ms | 5.07 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+01 | 5.35 ms | — | — | — | 3.48 ms | 6.69 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | 4.70 ms | — | — | — | 2.98 ms | 4.67 ms | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ~ shape 5e-16 | — | — | — | — | 3.93 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape 5e-16 | — | — | — | — | 2.85 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape 6e-16 | — | — | — | — | 3.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape 6e-16 | — | — | — | — | 3.69 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ 1e-15 | — | — | — | — | 3.41 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +3e+00 | — | — | — | — | 3.11 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +3e+00 | — | — | — | — | 5.69 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +3e+00 | — | — | — | — | 6.72 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +3e+00 | — | — | — | — | 6.42 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +3e+00 | — | — | — | — | 6.19 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +5e+00 | — | — | — | — | 2.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +5e+00 | — | — | — | — | 4.20 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | — | — | — | — | 3.10 ms | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ~ shape 5e-16 | — | — | — | — | 2.25 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape 5e-16 | — | — | — | — | 2.28 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape 6e-16 | — | — | — | — | 2.31 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape 6e-16 | — | — | — | — | 2.16 ms🏆 | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ 1e-15 | — | — | — | — | 2.22 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +3e+00 | — | — | — | — | 1.76 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +3e+00 | — | — | — | — | 4.42 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +3e+00 | — | — | — | — | 5.06 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +3e+00 | — | — | — | — | 5.06 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +3e+00 | — | — | — | — | 5.12 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +5e+00 | — | — | — | — | 2.57 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +5e+00 | — | — | — | — | 2.76 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | — | — | — | — | 2.51 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)