# `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_ensemble_bagging_pls_fit`. Reference: CRAN `enpls 6.1.1`. R roxygen note (`sklearn_extra.R::bagging_pls`): > Bagging PLS — formula entry point. ### 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_ensemble_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} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- bagging_pls_fit(X, Y, n_components, n_estimators = 50L, seed = 0L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- bagging_pls(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.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  ·  ⇄ 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✓ ref9.82 ms
Python · pls4all
pls4all.python✓ bind9.30 ms
pls4all.sklearn⇄ +2e-011.69 ms🏆
R · pls4all
pls4all.R⇄ +2e-014.62 ms
pls4all.R.formula⇄ +2e-016.41 ms
pls4all.R.mdatools⇄ +2e-015.11 ms
pls4all.R.pls⇄ +2e-014.93 ms
Python · external
📐ref.python_scikit_learnsource11.1 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref21.7 ms
Python · pls4all
pls4all.python✓ bind60.8 ms
pls4all.sklearn⇄ +2e-0111.4 ms🏆
R · pls4all
pls4all.R⇄ +2e-0125.2 ms
pls4all.R.formula⇄ +2e-0140.6 ms
pls4all.R.mdatools⇄ +2e-0146.3 ms
pls4all.R.pls⇄ +2e-0145.0 ms
Python · external
📐ref.python_scikit_learnsource56.1 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref27.8 ms
Python · pls4all
pls4all.python✓ bind12.7 ms
pls4all.sklearn⇄ +2e-012.54 ms🏆
R · pls4all
pls4all.R⇄ +2e-015.73 ms
pls4all.R.formula⇄ +2e-016.42 ms
pls4all.R.mdatools⇄ +2e-017.63 ms
pls4all.R.pls⇄ +2e-017.41 ms
Python · external
📐ref.python_scikit_learnsource14.2 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)