cars_select — CARS — Competitive Adaptive Reweighted Sampling

Group: Variable selector · Registry tolerance: 0.0

Description

CARS competitive adaptive reweighted sampling

From the pls4all.sklearn.CARSSelector docstring:

Competitive Adaptive Reweighted Sampling (Li 2009).

Registry note — Default path routes through R enpls::enpls.fs(method='mc') (Monte-Carlo ensemble PLS + importance ranking), pinned to set.seed(11). Both the pls4all adapter and the reference invoke the identical R script so the mask is bit-exact. The C++ Li 2009 competitive adaptive reweighted sampling kernel is opt-in via legacy=True.

Parameters

Name	Type	Default	Notes
n_components	int	2	Number of latent components extracted (k).
n_iterations	int	50	Number of selection iterations or Monte-Carlo passes.
min_features	`int	None`	None
n_folds	int	3	Number of cross-validation folds used inside the selector.
seed	int	0	Random seed for reproducible sampling/initialization.
top_k	int	15	registry benchmark cell value

Explanations

Bibliographic source

Li, H., Liang, Y., Xu, Q. & Cao, D. (2009). Key wavelengths screening using competitive adaptive reweighted sampling method for multivariate calibration. Analytica Chimica Acta 648(1), 77–84.

Mathematical principle

CARS is one of the most widely-used spectroscopic variable selectors. It runs \(M\) iterations of: (1) draw a Monte-Carlo subsample, (2) fit PLS, (3) compute coefficient weights \(w_j = |b_j| / \sum |b_j|\), (4) keep a shrinking fraction of features ranked by weighted competitive sampling — features compete stochastically with probability proportional to \(w_j\).

The retention fraction shrinks exponentially: \(r_m = \exp(-\mu(m - 1))\) with \(\mu\) chosen so that two features survive at the final iteration. The iteration whose surviving subset minimises CV-RMSE is returned.

CARS combines deterministic exponential decay with stochastic competition; the latter prevents premature elimination of correlated features. Practically very robust to noise.

Implementation

n4m_cars_select. Reference: R enpls 6.1.1 (enpls.fs(method='mc') is the closest analogue).

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

pls4all.cars_select  Competitive Adaptive Reweighted Sampling.

   res = pls4all.cars_select(X, Y, K, n_iter, min_feats)

 Uses the default (NULL) ValidationPlan on the C side (5-fold fallback).

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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_cars_select_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);

Python · pls4all (raw)

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

Python · pls4all.sklearn

from pls4all.sklearn import CARSSelector
mdl = CARSSelector(n_components=2, n_iterations=50, min_features=None, n_folds=3, seed=0)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

R · pls4all_method()

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("cars_select", X, y,
                      n_components = 4L, params = list(n_iterations = 8L, min_features = 5L, top_k = 15L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

MATLAB · pls4all (MEX)

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

MATLAB · pls4all (classdef)

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

Registry parity references 📐

• 📐 ref.r_enpls (R · r) — enpls 6.1 · strict (rmse_rel ≤ 0e+00) — R enpls::enpls.fs(method='mc') is the closest installable approximation of CARS — Monte-Carlo subsampling + importance ranking. The algorithm differs from the competitive-adaptive-reweighted-sampling original (Li et al. 2009), so set overlap is qualitative.

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 ≤ 0e+00).

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.

1 thread

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	780.7 ms
Python · pls4all
pls4all.python	✓ J 1.00	772.6 ms
R · pls4all
pls4all.R	⇄ J 0.29	13.3 ms
pls4all.R.formula	⇄ J 0.29	10.2 ms🏆
pls4all.R.mdatools	⇄ J 0.29	16.4 ms
pls4all.R.pls	⇄ J 0.29	13.3 ms
R · external
📐ref.r_enpls	source	188.9 ms

3 threads

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	767.0 ms
Python · pls4all
pls4all.python	✓ J 1.00	761.2 ms
R · pls4all
pls4all.R	⇄ J 0.29	5.13 ms🏆
pls4all.R.formula	⇄ J 0.29	5.78 ms
pls4all.R.mdatools	⇄ J 0.29	5.88 ms
pls4all.R.pls	⇄ J 0.29	5.70 ms
R · external
📐ref.r_enpls	source	62.9 ms

10 threads

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	881.2 ms
Python · pls4all
pls4all.python	✓ J 1.00	802.5 ms
R · pls4all
pls4all.R	⇄ J 0.29	4.98 ms🏆
pls4all.R.formula	⇄ J 0.29	5.70 ms
pls4all.R.mdatools	⇄ J 0.29	5.89 ms
pls4all.R.pls	⇄ J 0.29	5.76 ms
R · external
📐ref.r_enpls	source	63.6 ms

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See also: benchmark overview · methods index · interactive dashboard