# `boosting_pls` — Boosting PLS
_Group_: **Ensemble** · _Registry tolerance_: `1e-06`
## Description
Boosting PLS (§20)
From the `pls4all.sklearn.BoostingPLSRegression` docstring:
> Boosted PLS regression.
> **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` | `2` | Number of latent components extracted (k). |
| `n_estimators` | `int` | `50` | Number of base PLS sub-models in the ensemble. |
| `learning_rate` | `float` | `0.1` | Boosting shrinkage applied to each successive base learner. |
## 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.
### Mathematical principle
Gradient boosting builds an additive predictor $F_M(\mathbf{x}) = \sum_{m=1}^M \eta\, h_m(\mathbf{x})$ where each weak learner $h_m$ is fit on the negative gradient (the residuals, for squared-error loss) of the current ensemble. With PLS as the weak learner, each $h_m$ is a small ($k$-component) PLS fitted on the pseudo-response $r_i^{(m)} = y_i - F_{m-1}(\mathbf{x}_i)$.
The learning rate $\eta$ (typically 0.05–0.1) and the number of boosting iterations $M$ are the key hyperparameters; their product roughly controls the effective number of latent dimensions explored. Because boosting reduces bias, it can recover non-linear $Y$–$X$ relationships even with linear PLS base learners — at the cost of much higher computational cost than a single PLS.
### Implementation
`n4m_boosting_pls_fit`. Reference: CRAN `mboost::glmboost` with a PLS base learner (`mboost 2.9.11`).
### 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_boosting_pls_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 boosting_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = boosting_pls_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 BoostingPLSRegression
mdl = BoostingPLSRegression(n_components=2, n_estimators=50, learning_rate=0.1)
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("boosting_pls", X, y,
n_components = 4L, params = list(n_estimators = 10L, learning_rate = 0.1))
# 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.boosting_pls(X, y, 4);
% see header of bindings/matlab/+pls4all/boosting_pls.m for full
% parameter surface:
% res = boosting_pls(X, Y, n_components, n_estimators, learning_rate)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
```matlab
mdl = pls4all.fit("boosting_pls", X, y, "NumComponents", 4);
yhat = predict(mdl, Xtest);
```
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`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
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 | 2.52 ms🏆 | 1.13 ms🏆 | 13.2 ms | 55.1 ms | 1.31 ms | 2.82 ms | 6.07 ms | 52.7 ms | 272.6 ms | 26.9 ms | 277.6 ms | 1.4 s | 100.4 ms | 1.1 s |
pls4all.cpp.blas+omp | ≈ +2e-15 | 2.97 ms | 1.15 ms | 10.2 ms🏆 | 50.7 ms🏆 | 1.25 ms | 2.64 ms🏆 | 5.48 ms | 53.3 ms | 271.7 ms | 26.6 ms🏆 | 270.4 ms | 1.4 s🏆 | 106.0 ms | 1.2 s |
pls4all.cpp.omp | ≈ +2e-15 | 2.61 ms | 1.24 ms | 10.9 ms | 52.4 ms | 1.24 ms🏆 | 2.91 ms | 5.58 ms | 54.0 ms | 274.6 ms | 27.6 ms | 258.6 ms🏆 | 1.4 s | 98.8 ms🏆 | 1.1 s🏆 |
pls4all.cpp.ref | ≈ +2e-15 | 3.04 ms | 1.53 ms | 10.9 ms | 54.5 ms | 1.32 ms | 3.29 ms | 5.45 ms🏆 | 52.1 ms🏆 | 266.9 ms🏆 | 27.4 ms | 281.9 ms | 1.4 s | 113.0 ms | 1.1 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 3.02 ms | — | — | — | 1.37 ms | 2.67 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e+00 | 4.95 ms | — | — | — | 1.84 ms | 3.77 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e+00 | 15.9 ms | — | — | — | 4.33 ms | 13.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e+00 | 24.0 ms | — | — | — | 5.68 ms | 11.7 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e+00 | 23.7 ms | — | — | — | 5.85 ms | 11.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e+00 | 22.7 ms | — | — | — | 6.44 ms | 11.9 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +6e+00 | 4.81 ms | — | — | — | 2.36 ms | 4.55 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +6e+00 | 6.22 ms | — | — | — | 2.90 ms | 7.55 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mboost | source | 30.6 ms | — | — | — | 15.4 ms | 23.0 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 2e-15 | — | — | — | — | 2.14 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 2e-15 | — | — | — | — | 1.25 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 2e-15 | — | — | — | — | 1.59 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 2e-15 | — | — | — | — | 1.79 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.27 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e+00 | — | — | — | — | 1.85 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e+00 | — | — | — | — | 4.39 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e+00 | — | — | — | — | 6.41 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e+00 | — | — | — | — | 5.17 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e+00 | — | — | — | — | 4.91 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +6e+00 | — | — | — | — | 2.26 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +6e+00 | — | — | — | — | 2.91 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mboost | source | — | — | — | — | 16.1 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 2e-15 | — | — | — | — | 1.17 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 2e-15 | — | — | — | — | 1.19 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 2e-15 | — | — | — | — | 1.16 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 2e-15 | — | — | — | — | 1.21 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.06 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e+00 | — | — | — | — | 1.47 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e+00 | — | — | — | — | 3.13 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e+00 | — | — | — | — | 3.80 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e+00 | — | — | — | — | 3.91 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e+00 | — | — | — | — | 3.72 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +6e+00 | — | — | — | — | 2.11 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +6e+00 | — | — | — | — | 2.55 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mboost | source | — | — | — | — | 11.5 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)