# `group_sparse_pls` — Group-sparse PLS (Liquet 2016)
_Group_: **Sparse** · _Registry tolerance_: `1e-08`
## Description
Group sparse PLS (§7)
From the `pls4all.sklearn.GroupSparsePLSRegression` docstring:
> Group-sparse PLS — L1 across pre-declared feature groups.
> **Registry note** — R `sgPLS::gPLS` (Liquet et al. 2016, regression mode, scale=TRUE). pls4all's default kernel is a deterministic NumPy port of this algorithm (shared with `_GroupSparseNumpyReference`) and agrees with the R reference to ~1e-14. The original C++ soft-threshold-on-weights kernel is opt-in via `legacy=True`.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `group_assignment` | `—` | `None` | Integer array assigning each feature to a group (length n_features). |
| `group_lambda` | `float` | `0.05` | L1 penalty applied at the group level (group-sparse PLS). |
## Explanations
### Bibliographic source
Liquet, B., de Micheaux, P. L., Hejblum, B. P. & Thiébaut, R. (2016). *Group and sparse group partial least squares approaches applied in genomics context*. Bioinformatics 32(1), 35–42.
### Mathematical principle
When features partition into known groups — gene pathways, spectroscopic bands, biological assays — group-sparse PLS forces entire groups in or out together via a group-lasso penalty: $\mathcal{P}(\mathbf{w}) = \sum_g \sqrt{|g|}\,\|\mathbf{w}_g\|_2$, where $\mathbf{w}_g$ is the sub-vector of weights belonging to group $g$ and $|g|$ is its size. The $\ell_2$ norm inside the sum is non-differentiable at zero, which produces group-level sparsity (an entire $\mathbf{w}_g$ is either zero or non-zero).
Compared to plain sparse PLS, this gives a much more interpretable model when groups have biological meaning and avoids the situation where one or two members of a co-regulated cluster get selected while the rest don't.
Required input: a `group_assignment` vector mapping each feature to a group id.
### Implementation
`n4m_estimators_group_sparse_pls_fit`. Reference: CRAN `sgPLS 1.8.1`.
R roxygen note (`methods_extra.R::group_sparse_pls_fit`):
> Group-sparse PLS (group L1 across feature groups).
> @param n_components Integer. Number of latent components.
> @param group_assignment Method-specific parameter. See the underlying `*_fit()` function for the exact semantics.
> @param group_lambda Method-specific parameter. See the underlying `*_fit()` function for the exact semantics.
> @param X Numeric matrix of predictors (rows = samples, cols = features).
> @param Y Numeric matrix or vector of responses, with one row per sample.
> @export
MATLAB header (`bindings/matlab/+pls4all/group_sparse_pls.m`):
```text
pls4all.group_sparse_pls Group-sparse PLS (group L1 over feature groups).
```
### 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_estimators_group_sparse_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 group_sparse_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = group_sparse_pls_fit(ctx, cfg, X, y, n_components=4, group_assignment=groups)
# 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 GroupSparsePLSRegression
mdl = GroupSparsePLSRegression(n_components=2, group_assignment=None, group_lambda=0.05)
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("group_sparse_pls", X, y,
n_components = 4L, params = list(group_lambda = 0.1))
# 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 <- group_sparse_pls_fit(X, Y, n_components, group_assignment,
group_lambda = 0.05)
yhat <- pls4all_predict(res, X_test)
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
res = pls4all.group_sparse_pls(X, y, 4);
% see header of bindings/matlab/+pls4all/group_sparse_pls.m for full
% parameter surface:
% res = group_sparse_pls(X, Y, n_components, group_assignment, group_lambda)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("group_sparse_pls", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_numpy`** (python · python) — `numpy` in-tree · strict (rmse_rel ≤ 1e-08) — In-tree NumPy port of Liquet et al. 2016 group sparse PLS (R `sgPLS::gPLS`, regression mode, scale=TRUE). pls4all's default wrapper calls the same function, so the parity gate is bit-for-bit (max_abs < 1e-6). R `sgPLS::gPLS` is the published algorithmic counterpart and also matches to double-precision; the legacy C++ kernel (SIMPLS + soft-threshold-on-weights) is opt-in via ``legacy=True``.
- 📐 **`ref.r_sgpls`** (R · r) — `sgPLS` 1.8.1 · strict (rmse_rel ≤ 1e-08) — R `sgPLS::gPLS(X, Y, ncomp, ind.block.x, keepX=length(bnd))` (regression, scale=TRUE). The pls4all default kernel is a deterministic NumPy port of this algorithm and agrees to 1e-14 against this reference.
:::
### 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-08`).
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 | 200×50 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref | 8.36 ms |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 7.86 ms |
pls4all.sklearn | ⇄ +1e-01 | 3.79 ms |
| R · pls4all |
|---|
pls4all.R | ⇄ +1e-01 | 9.70 ms |
pls4all.R.formula | ⇄ +1e-01 | 11.0 ms |
pls4all.R.mdatools | ⇄ +1e-01 | 10.2 ms |
pls4all.R.pls | ⇄ +1e-01 | 11.0 ms |
| Python · external |
|---|
📐ref.python_numpy | source | 2.98 ms🏆 |
| R · external |
|---|
📐ref.r_sgpls | ⇄ +1e-15 | 33.7 ms |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 200×50 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref | 2.62 ms |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.76 ms |
pls4all.sklearn | ⇄ +1e-01 | 2.28 ms🏆 |
| R · pls4all |
|---|
pls4all.R | ⇄ +1e-01 | 8.78 ms |
pls4all.R.formula | ⇄ +1e-01 | 9.80 ms |
pls4all.R.mdatools | ⇄ +1e-01 | 11.9 ms |
pls4all.R.pls | ⇄ +1e-01 | 10.5 ms |
| Python · external |
|---|
📐ref.python_numpy | source | 3.11 ms |
| R · external |
|---|
📐ref.r_sgpls | ⇄ +1e-15 | 31.2 ms |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 200×50 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas+omp | ✓ ref | 2.91 ms |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.69 ms |
pls4all.sklearn | ⇄ +1e-01 | 2.53 ms🏆 |
| R · pls4all |
|---|
pls4all.R | ⇄ +1e-01 | 7.45 ms |
pls4all.R.formula | ⇄ +1e-01 | 9.19 ms |
pls4all.R.mdatools | ⇄ +1e-01 | 11.3 ms |
pls4all.R.pls | ⇄ +1e-01 | 8.50 ms |
| Python · external |
|---|
📐ref.python_numpy | source | 2.66 ms |
| R · external |
|---|
📐ref.r_sgpls | ⇄ +1e-15 | 26.7 ms |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)