pls_glm — PLS generalized linear regression

Group: Classification & GLM · Registry tolerance: 1e-06

Description

PLS-GLM (§5) — softmax/Poisson IRLS on PLS scores

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 native C++ kernel (legacy=True) runs the same algorithm.

Parameters

Name	Type	Default	Notes
n_components	int	4	registry benchmark cell value
n_targets	int	3	registry benchmark cell value
poisson	int	0	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. DOI 10.1016/j.csda.2004.02.005.

Mathematical principle

Component \(k\) weights column \(j\) by the coefficient of the deflated \(\mathbf X_j\) in the GLM of \(y\) on \((1,\mathbf t_1,\dots,\mathbf t_{k-1},\mathbf X_j)\); the normalized weights give the score \(\mathbf t_k\) and \(\mathbf X\) is deflated on it. A final GLM of \(y\) on \((1,\mathbf T)\) with the identity, log or logit link is folded back to the input scale through \(\mathbf W(\mathbf P^\top\mathbf W)^{-1}\).

Appropriate uses

Generalized linear regression of continuous (Gaussian), count (Poisson) or proportion (binomial) responses on many collinear spectral predictors.

Limits and validation

Weights come from one GLM fit per column and component, so the Poisson and binomial fits cost p IRLS solves per component; X is not scaled (plsRglm scaleX = FALSE), and separable binomial data make the logit coefficients diverge.

Implementation

One model per response column, as plsRglm with scaleX = FALSE: Gaussian weights use the closed-form partial regression, Poisson and binomial weights and the final score model use IRLS (at most max_iter steps, tolerance tol). Predictions are the mean response \(g^{-1}(\mathbf X\mathbf B+b_0)\).

Sources and provenance

Current implementation: cpp/src/core/extra_pls.cpp.

API and bindings

C ABI (ABI 2): n4m_estimators_pls_glm_fit. Use the linked public header for the exact signature, configuration, and result handles.

Python: no current AST-verified public n4m re-export was found for this method. The linked C ABI above is the documented surface in this checkout.

R (source-verified): pls_glm(formula, data, ncomp = 2L, family = "gaussian", na.action = stats::na.omit).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): pls_glm(X, Y, n_components, family).

The source signature has additional required inputs, so no example call is fabricated.

Registry parity references 📐

• 📐 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. The native n4m kernel implements the same algorithm (ABI 2.13).

Benchmarks

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

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 = archived binding-harness result 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). C++ and external rows show reference parity; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.

1 thread

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 1e-15	3.57 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	7.99 ms
pls4all.sklearn	⇄ +4e-01	2.74 ms🏆
R · archived pls4all benchmark
pls4all.R	⇄ +4e-01	7.97 ms
pls4all.R.formula	⇄ +4e-01	22.7 ms
pls4all.R.mdatools	⇄ +4e-01	25.8 ms
pls4all.R.pls	⇄ +4e-01	18.4 ms
R · external
📐ref.r_plsrglm	source	240.6 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 1e-15	3.56 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	8.04 ms
pls4all.sklearn	⇄ +4e-01	1.50 ms🏆
R · archived pls4all benchmark
pls4all.R	⇄ +4e-01	4.56 ms
pls4all.R.formula	⇄ +4e-01	5.18 ms
pls4all.R.mdatools	⇄ +4e-01	5.40 ms
pls4all.R.pls	⇄ +4e-01	5.24 ms
R · external
📐ref.r_plsrglm	source	138.8 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 1e-15	2.07 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.05 ms
pls4all.sklearn	⇄ +4e-01	1.46 ms🏆
R · archived pls4all benchmark
pls4all.R	⇄ +4e-01	3.78 ms
pls4all.R.formula	⇄ +4e-01	5.59 ms
pls4all.R.mdatools	⇄ +4e-01	4.89 ms
pls4all.R.pls	⇄ +4e-01	4.78 ms
R · external
📐ref.r_plsrglm	source	134.0 ms

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See also: benchmark overview · methods index · interactive dashboard