cars_select — CARS — Competitive Adaptive Reweighted Sampling

Group: Variable selector · Registry tolerance: 0.0

Description

CARS competitive adaptive reweighted sampling

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	current public binding signature
n_iterations	int	50	current public binding signature
min_features	int | None	None	current public binding signature
n_folds	int	3	current public binding signature
seed	int	0	current public binding signature
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. Verified primary link: https://doi.org/10.1016/j.aca.2009.06.046.

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.

Appropriate uses

Competitive wavelength reduction through repeated Monte Carlo PLS fits and adaptive elimination.

Limits and validation

CARS is stochastic and optimizes a validation criterion over many subsets, so nested or external validation is required.

Implementation

n4m_feature_selection_cars_select. Reference: R enpls 6.1.1 (enpls.fs(method='mc') is the closest analogue).

Sources and provenance

Current implementation: cpp/src/core/cars_selection.cpp.

API and bindings

C ABI (ABI 2): n4m_feature_selection_cars_select. Use the linked public header for the exact signature, configuration, and result handles.

Python (verified public re-export):

from n4m.feature_selection.wrapper import CARS

Source signature: CARS(*, n_components: int = 2, n_iterations: int = 50, min_features: int | None = None, n_folds: int = 3, seed: int = 0) (n4m/_impl/selection.py).

R (source-verified): cars_select(X, Y, n_components, n_iterations = 50L, min_features = 5L).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): cars_select(X, Y, n_components, n_iterations, min_features).

The source signature has additional required inputs, so no example call is fabricated.

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

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

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 = archived binding-harness result 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; archived language-harness rows 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 · archived pls4all benchmark
pls4all.python	✓ J 1.00	772.6 ms
R · archived pls4all benchmark
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 · archived pls4all benchmark
pls4all.python	✓ J 1.00	761.2 ms
R · archived pls4all benchmark
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 · archived pls4all benchmark
pls4all.python	✓ J 1.00	802.5 ms
R · archived pls4all benchmark
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