# `random_subspace_pls` — Random-subspace PLS
_Group_: **Ensemble** · _Registry tolerance_: `1e-06`
## Description
Random-subspace PLS (§20)
From the `pls4all.sklearn.RandomSubspacePLSRegression` docstring:
> Random-subspace PLS — Ho 1998.
> **Registry note** — sklearn `BaggingRegressor(PLSRegression(scale=False), max_features=k, bootstrap=False, bootstrap_features=False, max_samples=1.0)`. pls4all's default now mirrors this convention exactly (same RNG, feature-subset order, and prediction averaging), so the gate is bit-for-bit. The legacy single-pass C++ kernel (splitmix feature shuffle + 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. |
| `features_per_subspace` | `int` | `10` | Number of features randomly drawn per random-subspace base learner. |
| `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. |
## Explanations
### Bibliographic source
Ho, T. K. (1998). *The random subspace method for constructing decision forests*. IEEE TPAMI 20(8), 832–844. — adapted for PLS regressors.
### Mathematical principle
Each ensemble member fits PLS on a random subset of $m \ll p$ features. Compared to bagging (which randomises rows), random subspaces randomise **columns**, which is a much stronger variance-reduction mechanism for high-dimensional collinear data like NIR spectra: different subsets pick up different bands of the spectrum, and averaging across them smooths out band-specific noise.
Variance per member is higher than a full-feature PLS (less information per fit), but the ensemble average outperforms a single fit when the underlying truth is spread across many weakly-correlated features. Choosing $m \approx \sqrt{p}$ is a Breiman-style default; for spectra a more informed choice respects band widths.
Note that prediction on a new sample requires evaluating every member on **its own subset** of features, so the feature-index map must be stored per member.
### Implementation
`n4m_random_subspace_pls_fit`.
### 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_random_subspace_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 random_subspace_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = random_subspace_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 RandomSubspacePLSRegression
mdl = RandomSubspacePLSRegression(n_components=2, n_estimators=50, features_per_subspace=10, 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("random_subspace_pls", X, y,
n_components = 4L, params = list(n_estimators = 10L, features_per_subspace = 20L, 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.fit("random_subspace_pls", X, y, "NumComponents", 4);
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("random_subspace_pls", X, y, …)` directly from the unified MEX factory._
:::
::::
**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(), max_features=…, bootstrap=False)`. Random feature subspaces with full sample rows, matching pls4all's sampling shape. RNG differs from pls4all; qualitative 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 | ≈ | 11.7 ms🏆 | 14.8 ms | 23.4 ms | 70.4 ms | 10.4 ms | 14.8 ms | 21.7 ms | 71.4 ms | 293.6 ms | 62.5 ms | 328.9 ms | 1.6 s | 223.8 ms | 1.4 s🏆 |
pls4all.cpp.blas+omp | ≈ | 14.7 ms | 12.5 ms🏆 | 22.5 ms🏆 | 67.1 ms🏆 | 12.6 ms | 17.2 ms | 21.7 ms | 69.9 ms | 293.3 ms | 58.9 ms | 320.2 ms🏆 | 1.6 s🏆 | 217.6 ms🏆 | 1.5 s |
pls4all.cpp.omp | ≈ | 19.3 ms | 15.1 ms | 24.2 ms | 68.9 ms | 10.6 ms | 15.4 ms | 19.6 ms🏆 | 67.6 ms🏆 | 284.1 ms🏆 | 61.8 ms | 328.0 ms | 1.7 s | 231.0 ms | 1.5 s |
pls4all.cpp.ref | ≈ | 12.0 ms | 13.6 ms | 23.7 ms | 68.8 ms | 9.83 ms🏆 | 13.9 ms🏆 | 21.3 ms | 73.0 ms | 291.2 ms | 55.9 ms🏆 | 324.1 ms | 1.6 s | 222.8 ms | 1.5 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 13.8 ms | — | — | — | 10.6 ms | 14.6 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 3.32 ms | — | — | — | 1.84 ms | 3.87 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 13.2 ms | — | — | — | 5.10 ms | 12.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 24.7 ms | — | — | — | 5.05 ms | 9.66 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 21.9 ms | — | — | — | 5.99 ms | 12.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 27.9 ms | — | — | — | 6.48 ms | 11.6 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +7e+00 | 4.39 ms | — | — | — | 2.38 ms | 5.91 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +7e+00 | 5.04 ms | — | — | — | 2.91 ms | 5.31 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | 12.0 ms | — | — | — | 10.8 ms | 18.5 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 | — | — | — | — | 9.42 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 12.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 9.91 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 9.43 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 9.96 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +9e-01 | — | — | — | — | 1.73 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 3.95 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 5.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.01 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +7e+00 | — | — | — | — | 2.14 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +7e+00 | — | — | — | — | 2.68 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | — | — | — | — | 10.9 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 | — | — | — | — | 8.96 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 8.80 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 8.85 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 8.94 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 8.96 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +9e-01 | — | — | — | — | 1.47 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 3.41 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 4.06 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 3.82 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 3.77 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +7e+00 | — | — | — | — | 2.01 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +7e+00 | — | — | — | — | 2.39 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_scikit_learn | source | — | — | — | — | 9.30 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)