boosting_pls — Boosting PLS

Group: Ensemble · Registry tolerance: 1e-06

Description

Boosting PLS (§20)

Registry note — R mboost::glmboost(family=Gaussian()) — componentwise L2-Boost with a univariate linear base learner. pls4all’s default now mirrors this convention exactly (centred X, empirical Y-mean offset, greedy SSR-reduction feature selection), giving bit-for-bit parity. The original PLS-weak-learner boosting kernel is opt-in via legacy=True.

Parameters

Name	Type	Default	Notes
n_components	int	4	registry benchmark cell value
n_estimators	int	10	registry benchmark cell value
learning_rate	float	0.1	registry benchmark cell value

Explanations

Bibliographic source

Friedman, J. H. (2001). Greedy function approximation: a gradient boosting machine. Annals of Statistics 29(5), 1189–1232. — adapted for PLS as a base learner. Verified primary link: https://doi.org/10.1214/aos/1013203451.

Mathematical principle

Each round fits a linear PLS model to the current residual and adds its coefficient matrix, scaled by the learning rate, to the ensemble coefficient matrix. Algebraically, a sum of these base predictors is still one linear map from X to Y. Boosting can regularize the stagewise fit but does not introduce nonlinear features.

Appropriate uses

Stagewise fitting of linear PLS base learners to residuals when shrinkage across rounds improves stability.

Limits and validation

The summed coefficient vectors still define a linear predictor; this implementation cannot recover general nonlinear X–Y relations.

Implementation

The implementation stores the accumulated coefficients and intercept. Use kernel or explicitly nonlinear features when nonlinear response structure is required.

Sources and provenance

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

API and bindings

C ABI (ABI 2): n4m_ensemble_boosting_pls_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): boosting_pls(formula, data, ncomp = 2L, n_estimators = 50L, learning_rate = 0.1, na.action = stats::na.omit).

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

MATLAB / Octave (source-verified): boosting_pls(X, Y, n_components, n_estimators, learning_rate).

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

Registry parity references 📐

• 📐 ref.r_mboost (R · r) — mboost 2.9-11 · strict (rmse_rel ≤ 1e-06) — R mboost::glmboost(family=Gaussian()) — componentwise L2-Boost with univariate linear weak learners. pls4all’s default mirrors this exactly; bit-for-bit parity gate.

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 2e-15	1.23 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.52 ms
pls4all.sklearn	⇄ +2e+00	2.07 ms
R · archived pls4all benchmark
pls4all.R	⇄ +2e+00	5.05 ms
pls4all.R.formula	⇄ +2e+00	4.95 ms
pls4all.R.mdatools	⇄ +2e+00	6.92 ms
pls4all.R.pls	⇄ +2e+00	6.27 ms
R · external
📐ref.r_mboost	source	18.5 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	1.25 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.25 ms
pls4all.sklearn	⇄ +2e+00	1.79 ms
R · archived pls4all benchmark
pls4all.R	⇄ +2e+00	4.47 ms
pls4all.R.formula	⇄ +2e+00	4.80 ms
pls4all.R.mdatools	⇄ +2e+00	6.14 ms
pls4all.R.pls	⇄ +2e+00	5.37 ms
R · external
📐ref.r_mboost	source	16.4 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	1.27 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.70 ms
pls4all.sklearn	⇄ +2e+00	2.85 ms
R · archived pls4all benchmark
pls4all.R	⇄ +2e+00	9.14 ms
pls4all.R.formula	⇄ +2e+00	8.90 ms
pls4all.R.mdatools	⇄ +2e+00	11.2 ms
pls4all.R.pls	⇄ +2e+00	14.2 ms
R · external
📐ref.r_mboost	source	30.5 ms

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See also: benchmark overview · methods index · interactive dashboard