# `bagging_pls` — Bagging PLS
_Group_: **Ensemble** · _Registry tolerance_: `1e-06`
## Description
Bagging PLS (§20)
From the `pls4all.sklearn.BaggingPLSRegression` docstring:
> Bagged PLS (Breiman 1996).
> **Registry note** — sklearn `BaggingRegressor(PLSRegression(scale=False), bootstrap=True, max_samples=1.0)`. pls4all's default now mirrors this convention exactly (same RNG, bootstrap-index order, and prediction averaging), so the gate is bit-for-bit. The legacy single-pass C++ kernel (splitmix bootstrap + coefficient averaging) 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. |
| `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. |
## Explanations
### Bibliographic source
Breiman, L. (1996). *Bagging predictors*. Machine Learning 24(2), 123–140. — adapted for PLS by various chemometric authors.
### Mathematical principle
Bootstrap aggregating draws $B$ bootstrap samples $\{(\mathbf{X}^{(b)}, \mathbf{y}^{(b)})\}_{b=1}^{B}$ from the calibration set (sampling with replacement, $n$ rows each), fits a PLS model on each, and averages the predictions: $\hat{y}_{\mathrm{bag}}(\mathbf{x}) = \frac{1}{B}\sum_b \hat{y}^{(b)}(\mathbf{x})$.
PLS is a high-bias / low-variance learner, so bagging rarely beats a single well-tuned PLS in pure RMSE. Its real value is **inferential**: the bootstrap distribution of coefficients gives non-parametric standard errors and confidence intervals that are otherwise inaccessible. The per-bag $\mathbf{B}^{(b)}$ matrices form an empirical distribution from which posterior intervals on each feature's contribution can be read off.
Computational cost: $B$ times a single fit, embarrassingly parallel. Use $B \in [50, 500]$ depending on how stable the CIs need to be.
### Implementation
`n4m_bagging_pls_fit`. Reference: CRAN `enpls 6.1.1`.
### 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_bagging_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 bagging_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = bagging_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 BaggingPLSRegression
mdl = BaggingPLSRegression(n_components=2, n_estimators=50, seed=0)
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("bagging_pls", X, y,
n_components = 4L, params = list(n_estimators = 10L, seed = 42L))
# 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.bagging_pls(X, y, 4);
% see header of bindings/matlab/+pls4all/bagging_pls.m for full
% parameter surface:
% res = bagging_pls(X, Y, n_components, n_estimators, seed)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
```matlab
mdl = pls4all.fit("bagging_pls", X, y, "NumComponents", 4);
yhat = predict(mdl, Xtest);
```
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_scikit_learn`** (python · python) — `scikit-learn` 1.8.0 · strict (rmse_rel ≤ 1e-06) — sklearn `BaggingRegressor(PLSRegression(scale=False), bootstrap=True, max_samples=1.0)`. pls4all wraps the same sklearn objects, giving bit-for-bit parity.
:::
### 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 | ≈ | 14.1 ms | 20.1 ms🏆 | 40.7 ms🏆 | 159.2 ms | 9.92 ms🏆 | 17.0 ms | 30.0 ms | 161.8 ms🏆 | 1.1 s | 79.5 ms | 1.1 s🏆 | 7.1 s | 360.2 ms | 5.5 s |
pls4all.cpp.blas+omp | ≈ | 14.1 ms🏆 | 23.4 ms | 44.7 ms | 151.7 ms🏆 | 11.0 ms | 21.3 ms | 33.2 ms | 167.2 ms | 904.1 ms🏆 | 83.0 ms | 1.1 s | 7.3 s | 355.6 ms | 5.4 s🏆 |
pls4all.cpp.omp | ≈ | 14.2 ms | 22.7 ms | 41.3 ms | 161.0 ms | 12.0 ms | 19.7 ms | 30.8 ms | 163.8 ms | 1.0 s | 76.9 ms | 1.1 s | 7.3 s | 338.1 ms🏆 | 5.5 s |
pls4all.cpp.ref | ≈ | 16.5 ms | 21.0 ms | 42.1 ms | 154.1 ms | 10.1 ms | 16.6 ms | 27.9 ms🏆 | 167.8 ms | 1.1 s | 75.9 ms🏆 | 1.2 s | 6.9 s🏆 | 356.6 ms | 5.7 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 14.9 ms | — | — | — | 10.4 ms | 13.0 ms🏆 | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +9e-01 | 3.93 ms | — | — | — | 1.82 ms | 3.80 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +9e-01 | 17.1 ms | — | — | — | 5.10 ms | 15.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +9e-01 | 27.0 ms | — | — | — | 5.44 ms | 10.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +9e-01 | 22.4 ms | — | — | — | 5.28 ms | 11.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +9e-01 | 23.0 ms | — | — | — | 6.02 ms | 12.3 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | 4.80 ms | — | — | — | 2.38 ms | 6.33 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | 5.47 ms | — | — | — | 3.24 ms | 5.55 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | 14.5 ms | — | — | — | 10.8 ms | 13.3 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 | — | — | — | — | 11.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 10.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 10.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 9.90 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 9.87 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e-01 | — | — | — | — | 2.58 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e-01 | — | — | — | — | 4.24 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e-01 | — | — | — | — | 5.63 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e-01 | — | — | — | — | 5.20 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e-01 | — | — | — | — | 4.99 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 2.47 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 3.39 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | — | — | — | — | 11.0 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 | — | — | — | — | 8.81 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 8.79 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 9.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 8.98 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 8.85 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +2e-01 | — | — | — | — | 1.50 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +2e-01 | — | — | — | — | 3.21 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +2e-01 | — | — | — | — | 4.00 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +2e-01 | — | — | — | — | 3.70 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +2e-01 | — | — | — | — | 4.03 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 2.08 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 3.28 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | — | — | — | — | 9.52 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)