# `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_estimators_pls_glm_fit`. Reference: R `plsRglm 1.7.0`. R roxygen note (`sklearn_methods.R::pls_glm`): > PLS-GLM — formula entry point. Default is Gaussian; set > `family = "poisson"` for Poisson IRLS. 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_estimators_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} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- pls_glm_fit(X, Y, n_components, poisson = FALSE) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- pls_glm(y ~ ., data = train, ncomp = 4L) yhat <- predict(fit, newdata = test) summary(fit) ``` ::: :::{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  ·  ⇄ 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-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
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 1e-153.57 ms
Python · pls4all
pls4all.python✓ bind7.99 ms
pls4all.sklearn⇄ +4e-012.74 ms🏆
R · pls4all
pls4all.R⇄ +4e-017.97 ms
pls4all.R.formula⇄ +4e-0122.7 ms
pls4all.R.mdatools⇄ +4e-0125.8 ms
pls4all.R.pls⇄ +4e-0118.4 ms
R · external
📐ref.r_plsrglmsource240.6 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 1e-153.56 ms
Python · pls4all
pls4all.python✓ bind8.04 ms
pls4all.sklearn⇄ +4e-011.50 ms🏆
R · pls4all
pls4all.R⇄ +4e-014.56 ms
pls4all.R.formula⇄ +4e-015.18 ms
pls4all.R.mdatools⇄ +4e-015.40 ms
pls4all.R.pls⇄ +4e-015.24 ms
R · external
📐ref.r_plsrglmsource138.8 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 1e-152.07 ms
Python · pls4all
pls4all.python✓ bind2.05 ms
pls4all.sklearn⇄ +4e-011.46 ms🏆
R · pls4all
pls4all.R⇄ +4e-013.78 ms
pls4all.R.formula⇄ +4e-015.59 ms
pls4all.R.mdatools⇄ +4e-014.89 ms
pls4all.R.pls⇄ +4e-014.78 ms
R · external
📐ref.r_plsrglmsource134.0 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)