# `pls_glm` — PLS-GLM (Generalised Linear Model PLS)
_Group_: **Classification & GLM** · _Registry tolerance_: `1e-06`
## Description
PLS-GLM (§5) — softmax/Poisson IRLS on PLS scores
From the `pls4all.sklearn.PLSGLMRegressor` docstring:
> PLS + Generalised Linear Model head (Bastien 2005).
> **Registry note** — R `plsRglm::plsRglm` (Bastien, Vinzi & Tenenhaus 2005) with `scaleX=FALSE`. pls4all's default now mirrors the plsRglm algorithm exactly: per-component partial-regression weights (Gaussian-identity uses closed-form OLS; Poisson-log uses IRLS), score-space GLM coefficients, and per-target stacking. The legacy single-pass C++ kernel (centred SIMPLS + column-mean intercept) is opt-in via ``legacy=True``.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `poisson` | `bool` | `False` | If True, fit a Poisson-deviance PLS-GLM (default Gaussian link). |
| `n_targets` | `int` | `3` | registry benchmark cell value |
## Explanations
### Bibliographic source
Marx, B. D. (1996). *Iteratively reweighted partial least squares estimation for generalized linear regression*. Technometrics 38(4), 374–381.
### Mathematical principle
PLS-GLM generalises PLS-logistic to any GLM family. The IRLS recipe is identical — derive a working response from the current linear predictor, fit PLS with the GLM weights, iterate — but the link function varies: identity for Gaussian, log for Poisson, logit for Bernoulli/binomial.
pls4all currently supports Gaussian and Poisson families (controlled by the `poisson` flag). The Poisson case is useful for count regression on spectroscopy data where the response is an integer abundance (cell counts, particle counts) rather than a continuous concentration.
Compared to running a vanilla PLS on $\log(y+1)$, the true Poisson formulation correctly handles the mean–variance relationship and is less biased for low counts.
### Implementation
`n4m_pls_glm_fit`. Reference: R `plsRglm 1.7.0`.
MATLAB header (`bindings/matlab/+pls4all/GlmRegression.m`):
```text
pls4all.GlmRegression — PLS-GLM (Gaussian / Poisson IRLS).
Like MB-PLS, uses the stored intercept directly.
```
### 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_glm_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_glm_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = pls_glm_fit(ctx, cfg, X, y, n_components=4)
# 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 PLSGLMRegressor
mdl = PLSGLMRegressor(n_components=2, poisson=False)
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_glm", X, y,
n_components = 4L, params = list(n_targets = 3L, poisson = 0L))
# 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_glm(X, y, 4);
% see header of bindings/matlab/+pls4all/pls_glm.m for full
% parameter surface:
% res = pls_glm(X, Y, n_components, family)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
```matlab
mdl = pls4all.fit("pls_glm", X, y, "NumComponents", 4);
yhat = predict(mdl, Xtest);
```
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_plsrglm`** (R · r) — `plsRglm` 1.5.1 · strict (rmse_rel ≤ 1e-06) — R `plsRglm::plsRglm` (Bastien, Vinzi & Tenenhaus 2005) with the `pls-glm-gaussian` / `pls-glm-poisson` family. pls4all implements a simpler PLS-then-link variant so predictions diverge substantially; the parity check is a presence flag for the external reference.
:::
### 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**: strict — numeric equivalence (`rmse_rel_tol ≤ 1e-06`).
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) | 200×30 (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 | ≈ +2e-15 | 4.38 ms | 2.18 ms🏆 | 16.8 ms | 119.1 ms | 2.06 ms | 3.78 ms🏆 | 8.52 ms | 115.0 ms | 768.5 ms | 49.0 ms🏆 | 757.6 ms | 4.5 s | 290.6 ms | 3.6 s |
pls4all.cpp.blas+omp | ≈ +2e-15 | 4.25 ms | 2.80 ms | 17.2 ms | 111.4 ms | 2.15 ms | 4.66 ms | 9.13 ms | 111.2 ms | 746.1 ms | 49.6 ms | 731.4 ms | 4.4 s🏆 | 266.3 ms🏆 | 3.6 s |
pls4all.cpp.omp | ≈ +2e-15 | 4.29 ms | 2.70 ms | 17.2 ms | 119.8 ms | 2.21 ms | 3.86 ms | 7.10 ms🏆 | 112.3 ms | 749.3 ms | 49.4 ms | 725.2 ms🏆 | 4.5 s | 295.9 ms | 3.6 s |
pls4all.cpp.ref | ≈ +2e-15 | 4.09 ms🏆 | 2.52 ms | 16.3 ms🏆 | 109.3 ms🏆 | 2.05 ms🏆 | 3.99 ms | 8.37 ms | 109.1 ms🏆 | 737.4 ms🏆 | 52.2 ms | 733.2 ms | 4.5 s | 280.8 ms | 3.5 s🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 4.65 ms | — | — | — | 2.35 ms | 4.67 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +4e-01 | 5.27 ms | — | — | — | 1.78 ms | 4.16 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +3e-01 | 13.9 ms | — | — | — | 4.71 ms | 9.98 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +3e-01 | 24.5 ms | — | — | — | 7.08 ms | 12.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +3e-01 | 22.3 ms | — | — | — | 5.84 ms | 11.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +3e-01 | 21.8 ms | — | — | — | 5.42 ms | 14.5 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | 4.49 ms | — | — | — | 2.12 ms | 4.14 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | 4.66 ms | — | — | — | 2.69 ms | 5.57 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsrglm | source | 615.0 ms | — | — | — | 127.9 ms | 251.4 ms | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (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 | ✓ ref 1e-15 | — | — | — | — | 2.07 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 1e-15 | — | — | — | — | 2.18 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 1e-15 | — | — | — | — | 2.82 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 1e-15 | — | — | — | — | 2.14 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.05 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +4e-01 | — | — | — | — | 1.50 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +3e-01 | — | — | — | — | 3.92 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +3e-01 | — | — | — | — | 5.76 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +3e-01 | — | — | — | — | 4.75 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +3e-01 | — | — | — | — | 4.70 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 2.04 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 3.02 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsrglm | source | — | — | — | — | 122.5 ms | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (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 | ✓ ref 1e-15 | — | — | — | — | 1.85 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 1e-15 | — | — | — | — | 1.85 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 1e-15 | — | — | — | — | 1.83 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 1e-15 | — | — | — | — | 1.89 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.90 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +4e-01 | — | — | — | — | 1.35 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +3e-01 | — | — | — | — | 3.48 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +3e-01 | — | — | — | — | 4.03 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +3e-01 | — | — | — | — | 3.63 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +3e-01 | — | — | — | — | 3.91 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 1.90 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 2.30 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsrglm | source | — | — | — | — | 97.2 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)