sparse_simpls — Sparse SIMPLS (Chun & Keleş 2010)

Group: Sparse · Registry tolerance: 1.0

Description

Sparse SIMPLS with soft-threshold lambda

From the pls4all.sklearn.SparseSimplsRegression docstring:

Sparse SIMPLS with soft-thresholded weights (Chun & Keles 2010).

Registry note — R spls 2.3.2 (Chun & Keles 2010) is the canonical external reference. The in-tree NumPy port SparseSimplsPythonReference provides a hermetic alternative when R is unavailable.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

sparsity_lambda

float

0.05

L1 soft-threshold magnitude applied to the PLS weight vectors.

Explanations

Bibliographic source

Chun, H. & Keleş, S. (2010). Sparse partial least squares regression for simultaneous dimension reduction and variable selection. JRSS B 72(1), 3–25.

Mathematical principle

Sparse PLS adds a soft-thresholding step to each SIMPLS loading weight so that the latent direction is supported on only a small subset of features. Mathematically, after the un-thresholded weight \(\mathbf{w}\) is computed, we solve \(\mathbf{w}^{\star} = \arg\min_{\|\mathbf{c}\|=1} \|\mathbf{c} - \mathbf{w}\|_2^2 + \lambda \|\mathbf{c}\|_1\), which has the closed-form soft-threshold solution \(c_j = \operatorname{sign}(w_j)\,(|w_j| - \lambda/2)_+\) followed by re-normalisation.

The penalty \(\lambda\) controls sparsity: small \(\lambda\) approaches standard PLS, large \(\lambda\) zeroes most weights. In high-dimensional (\(p \gg n\)) spectroscopy or omics data, sparse PLS simultaneously builds the latent predictive direction and selects the variables that support it — a much cleaner story than running PLS then thresholding coefficients post-hoc.

The Chun & Keleş formulation differs subtly from the earlier Lê Cao 2008 sPLS (used in mixOmics): Chun & Keleş threshold the un-deflated weight while Lê Cao threshold the deflated weight at each iteration. pls4all implements the Chun & Keleş formulation.

Implementation

n4m_sparse_simpls_fit. Reference: CRAN spls 2.3.2 (Chun & Keleş authors). No widely installable Python port exists with this exact normalisation convention.

MATLAB header (bindings/matlab/+pls4all/SparsePlsRegression.m):

pls4all.SparsePlsRegression — Sparse SIMPLS (Chun & Keles 2010)
 as a tier-2 classdef. Construct via the factory:

   mdl = pls4all.fitrsparsepls(X, y, "NumComponents", 5, "Lambda", 0.05)

 or directly:

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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_sparse_simpls_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);

import pls4all
from pls4all._methods import sparse_simpls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = sparse_simpls_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import SparseSimplsRegression
mdl = SparseSimplsRegression(n_components=2, sparsity_lambda=0.05)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("sparse_simpls", X, y,
                      n_components = 4L, params = list(sparsity_lambda = 0.05))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.sparse_simpls(X, y, 4);
% see header of bindings/matlab/+pls4all/sparse_simpls.m for full
% parameter surface:
%   res = sparse_simpls(X, Y, n_components, sparsity_lambda)
yhat = predict(res, Xtest);

mdl  = pls4all.fit("sparse_simpls", X, y, "NumComponents", 4);
yhat = predict(mdl, Xtest);

Registry parity references 📐

  • 📐 ref.python_chun_keles_spls (python · python) — chun_keles_spls 1.0 · qualitative (rmse_rel ≤ 1e+00) — In-tree NumPy port of Chun & Keles 2010 sparse PLS (the default pls2 / simpls configuration of R spls::spls). Verified against the R 2.3.2 package on the parity cells.

  • 📐 ref.r_spls (R · r) — spls 2.3.2 · qualitative (rmse_rel ≤ 1e+00) — R spls 2.3.2 (Chun & Keles). Predicts via the regression coefficient matrix from sparse-thresholded SIMPLS.

Benchmarks

Adaptive wall-clock per cell measured against full_matrix.csv. 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). 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.

BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-161.89 ms
Python · pls4all
pls4all.python✓ bind1.93 ms
pls4all.sklearn✓ bind1.88 ms🏆
R · pls4all
pls4all.R✓ 5e-154.60 ms
pls4all.R.formula✓ 5e-155.64 ms
pls4all.R.mdatools✓ 5e-156.30 ms
pls4all.R.pls✓ 5e-155.36 ms
Python · external
📐ref.python_chun_keles_splssource3.55 ms
R · external
📐ref.r_spls⇄ +6e-1513.4 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-161.93 ms
Python · pls4all
pls4all.python✓ bind1.87 ms🏆
pls4all.sklearn✓ bind1.92 ms
R · pls4all
pls4all.R✓ 5e-154.97 ms
pls4all.R.formula✓ 5e-156.05 ms
pls4all.R.mdatools✓ 5e-156.32 ms
pls4all.R.pls✓ 5e-155.77 ms
Python · external
📐ref.python_chun_keles_splssource3.54 ms
R · external
📐ref.r_spls⇄ +6e-1512.8 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-161.91 ms🏆
Python · pls4all
pls4all.python✓ bind1.98 ms
pls4all.sklearn✓ bind1.95 ms
R · pls4all
pls4all.R✓ 5e-154.83 ms
pls4all.R.formula✓ 5e-155.49 ms
pls4all.R.mdatools✓ 5e-156.00 ms
pls4all.R.pls✓ 5e-155.74 ms
Python · external
📐ref.python_chun_keles_splssource3.58 ms
R · external
📐ref.r_spls⇄ +6e-1512.0 ms

See also: benchmark overview · methods index · interactive dashboard