variable_select_coef — Coefficient-magnitude selection

Group: Variable selector · Registry tolerance: 1.1

Description

|Coef| top-k selection (§18 Phase 5a, method=1)

From the pls4all.sklearn.CoefficientSelector docstring:

|coef| top-k selector. Ranks features by the magnitude of their PLS regression coefficient on Y.

Registry note — R pls::plsr(method='simpls') |coef| ranking. The solver mismatch is fixed, but residual top-k drift remains because pls4all ranks its stored C-kernel coefficient vector while R reconstructs coefficients through pls’s SIMPLS convention. Mask RMSE-rel ~0=perfect, ~1=half disagree, ~1.41=disjoint; tolerance accepts this known coefficient-convention divergence.

Parameters

Name

Type

Default

Notes

top_k

int

None

Number of features to retain.

n_components

int

2

Number of latent components extracted (k).

solver

str

'simpls'

Inner algorithm: ‘nipals’, ‘simpls’, ‘svd’, ‘kernel’, ‘orthogonal-scores’, ‘power’, ‘randomized-svd’, ‘wide-kernel’.

center_x

bool

True

Subtract the column mean of X before fitting.

scale_x

bool

True

Standardize X columns to unit variance before fitting.

tol

float

1e-06

Convergence tolerance for iterative solvers (NIPALS / power-iteration).

max_iter

int

500

Maximum iterations for iterative solvers.

Explanations

Bibliographic source

Martens, H. & Næs, T. (1989). Multivariate Calibration, §5. — the simplest ranking baseline.

Mathematical principle

Rank features by the absolute magnitude of their PLS regression coefficient \(|b_j|\) in the original feature scale. Pick the top-\(k\) as the selected subset.

This is the simplest possible PLS variable selector. It is biased — features with large variance get smaller coefficients for the same predictive effect — so it should usually be applied after autoscaling to remove the variance-induced bias. Once autoscaled, \(|b_j|\) ranks features by their standardised partial effect on \(y\), which is statistically meaningful.

Useful as a sanity-check baseline against more sophisticated selectors. If a complex method does not beat coefficient-magnitude selection, it is probably over-engineered.

Implementation

n4m_variable_select_rank with metric=COEF.

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

pls4all.coefficient_select  Coefficient-magnitude feature ranking.

   res = pls4all.coefficient_select(X, Y, n_components, top_k)

 Fits an internal SIMPLS model and ranks features by the magnitude of
 their regression coefficients.

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

from pls4all.sklearn import CoefficientSelector
mdl = CoefficientSelector(top_k, n_components=2, solver='simpls', center_x=True, scale_x=True, tol=1e-06, max_iter=500)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("variable_select_coef", X, y,
                      n_components = 4L, params = list(top_k = 10L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

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

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

Registry parity references 📐

  • 📐 ref.r_pls (R · r) — pls 2.8.5 · qualitative (rmse_rel ≤ 1e+00) — R pls::plsr coefficient magnitudes — top-k indices ranked by |coef|. Mirrors method=1 of pls4all’s ranker.

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: qualitative — shape/smoke comparison only. The external library and pls4all do not produce numerically equivalent output for this method (see the MethodSpec notes); the rmse_rel_tol ≤ 1e+00 budget is set wide on purpose. Treat ~ shape as “we ran both, both finished”, not as numerical agreement.

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.

BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.001.56 ms🏆
Python · pls4all
pls4all.python✓ J 1.001.61 ms
pls4all.sklearn✓ J 1.002.87 ms
R · pls4all
pls4all.R✓ J 1.0015.0 ms
pls4all.R.formula✓ J 1.009.19 ms
pls4all.R.mdatools✓ J 1.0018.1 ms
pls4all.R.pls✓ J 1.0017.2 ms
R · external
📐ref.r_plssource50.9 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.0011.3 ms
Python · pls4all
pls4all.python✓ J 1.006.88 ms🏆
pls4all.sklearn✓ J 1.007.62 ms
R · pls4all
pls4all.R✓ J 1.0016.9 ms
pls4all.R.formula✓ J 1.0018.4 ms
pls4all.R.mdatools✓ J 1.009.25 ms
pls4all.R.pls✓ J 1.0017.5 ms
R · external
📐ref.r_plssource16.3 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.001.87 ms
Python · pls4all
pls4all.python✓ J 1.002.60 ms
pls4all.sklearn✓ J 1.001.86 ms🏆
R · pls4all
pls4all.R✓ J 1.005.27 ms
pls4all.R.formula✓ J 1.006.03 ms
pls4all.R.mdatools✓ J 1.006.17 ms
pls4all.R.pls✓ J 1.006.23 ms
R · external
📐ref.r_plssource16.5 ms

See also: benchmark overview · methods index · interactive dashboard