fused_sparse_pls — Fused-sparse PLS

Group: Sparse · Registry tolerance: 0.05 · Parity reference: paper-only (Yengo, L., Jacques, J., Biernacki, C. & Canouil, M. (2016). Variable clustering in high-dimensional linear regression: The R package clere. R Journal 8(1), 92-106. (Fused-sparse PLS variants have no widely installable R / Python port.))

Description

Fused sparse PLS (§7)

From the pls4all.sklearn.FusedSparsePLSRegression docstring:

Fused-sparse PLS — L1 + adjacent-coef smoothing.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

l1_lambda

float

0.05

L1 sparsity penalty for fused-sparse PLS.

fusion_lambda

float

0.05

Fused-lasso penalty enforcing smoothness between adjacent coefficients.

Explanations

Bibliographic source

Tibshirani, R., Saunders, M., Rosset, S., Zhu, J. & Knight, K. (2005). Sparsity and smoothness via the fused lasso. JRSS B 67(1), 91–108. — generalised to PLS loadings.

Mathematical principle

The fused lasso penalty combines L1 sparsity with an L1 penalty on first differences of neighbouring coefficients: \(\mathcal{P}(\mathbf{w}) = \lambda_1 \|\mathbf{w}\|_1 + \lambda_2 \sum_{j=1}^{p-1}|w_{j+1} - w_j|\). For spectroscopic data this is uniquely useful: the second term encourages neighbouring wavelengths to share a coefficient, which produces piecewise-constant loadings reflecting the underlying band structure of the spectrum rather than the choppy sample-noise pattern that plain L1 alone produces.

Tuning two penalties simultaneously is non-trivial: \(\lambda_1\) controls overall sparsity, \(\lambda_2\) controls within-band smoothness. Plotting the selected wavelength bands as a function of \(\lambda_2\) at fixed sparsity is a common diagnostic.

Computationally the fused-lasso step is a 1-D total variation denoising problem with a closed-form taut-string solution in \(O(p)\); pls4all uses Condat’s algorithm.

Implementation

n4m_fused_sparse_pls_fit. No widely installable reference library — sgPLS covers group-sparse but not fused-sparse. Documented as paper_only in the registry.

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

pls4all.fused_sparse_pls  Fused-sparse PLS (L1 + adjacent-coef smoothing).

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_fused_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);

import pls4all
from pls4all._methods import fused_sparse_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = fused_sparse_pls_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 FusedSparsePLSRegression
mdl = FusedSparsePLSRegression(n_components=2, l1_lambda=0.05, fusion_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("fused_sparse_pls", X, y,
                      n_components = 4L, params = list(l1_lambda = 0.05, fusion_lambda = 0.1))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.fused_sparse_pls(X, y, 4);
% see header of bindings/matlab/+pls4all/fused_sparse_pls.m for full
% parameter surface:
%   res = fused_sparse_pls(X, Y, n_components, l1_lambda, fusion_lambda)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("fused_sparse_pls", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📜 Paper-only — no executable parity reference; the pls4all implementation is verified by a smoke fit only. Canonical citation: Yengo, L., Jacques, J., Biernacki, C. & Canouil, M. (2016). Variable clustering in high-dimensional linear regression: The R package clere. R Journal 8(1), 92-106. (Fused-sparse PLS variants have no widely installable R / Python port.)

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 🏆.

BackendParity200×50 (ms)
Python · pls4all
pls4all.python✓ bind1.95 ms🏆
pls4all.sklearn✓ bind2.13 ms
R · pls4all
pls4all.R✓ bind6.13 ms
pls4all.R.formula✓ bind7.70 ms
pls4all.R.mdatools✓ bind7.55 ms
pls4all.R.pls✓ bind7.80 ms
BackendParity200×50 (ms)
Python · pls4all
pls4all.python✓ bind1.88 ms🏆
pls4all.sklearn✓ bind2.09 ms
R · pls4all
pls4all.R✓ bind6.14 ms
pls4all.R.formula✓ bind7.73 ms
pls4all.R.mdatools✓ bind8.04 ms
pls4all.R.pls✓ bind7.53 ms
BackendParity200×50 (ms)
Python · pls4all
pls4all.python✓ bind1.97 ms🏆
pls4all.sklearn✓ bind2.02 ms
R · pls4all
pls4all.R✓ bind6.56 ms
pls4all.R.formula✓ bind8.64 ms
pls4all.R.mdatools✓ bind8.07 ms
pls4all.R.pls✓ bind8.65 ms

See also: benchmark overview · methods index · interactive dashboard