# `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` | Minimum number of variables the selector is allowed to keep (defaults to `n_components`). |
| `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`):
```text
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**
::::{tab-set}
:class: pls4all-bindings
:::{tab-item} C ABI · libn4m
:sync: c
:class-label: lang-c
```c
/* 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);
```
:::
:::{tab-item} Python · pls4all (raw)
:sync: python-raw
:class-label: lang-python
```python
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"), …
```
:::
:::{tab-item} Python · pls4all.sklearn
:sync: python-sklearn
:class-label: lang-python
```python
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)
```
:::
:::{tab-item} R · pls4all_method()
:sync: r-dispatcher
:class-label: lang-r
```r
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.
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
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);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("cars_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`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`](../benchmarks/overview.md). 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 · ✗ 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`](../benchmarks/methodology.md)). 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.
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ≈ | 1.0 s | 6.9 s | 10.6 s | 42.4 s | 843.7 ms | 892.8 ms | 6.8 s | 15.0 s | 65.5 s | 9.8 s | 52.0 s | 268.9 s | 24.9 s🏆 | 183.5 s🏆 |
pls4all.cpp.blas+omp | ≈ | 1.1 s | 6.4 s🏆 | 10.6 s | 43.2 s | 859.2 ms | 890.5 ms | 6.5 s | 15.0 s | 63.8 s🏆 | 9.2 s🏆 | 48.4 s | 262.3 s🏆 | 28.2 s | 196.4 s |
pls4all.cpp.omp | ≈ | 1.1 s | 6.7 s | 10.3 s🏆 | 42.8 s | 861.7 ms | 889.3 ms | 6.9 s | 14.6 s | 74.5 s | 9.3 s | 54.9 s | 295.4 s | 26.7 s | 198.5 s |
pls4all.cpp.ref | ≈ | 1.0 s | 6.9 s | 10.7 s | 42.3 s🏆 | 853.5 ms | 881.2 ms | 6.4 s🏆 | 14.1 s🏆 | 70.3 s | 9.3 s | 48.2 s🏆 | 294.7 s | 27.6 s | 193.3 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 1.1 s | — | — | — | 853.9 ms | 895.8 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ⚠ | — | — | — | — | — | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 13.2 ms | — | — | — | 4.95 ms | 12.9 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 24.0 ms | — | — | — | 7.25 ms | 10.5 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 21.5 ms | — | — | — | 6.52 ms | 11.7 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 25.3 ms | — | — | — | 6.47 ms | 9.54 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.01 ms | — | — | — | 3.28 ms | 5.61 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 9.19 ms | — | — | — | 4.05 ms | 5.53 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_enpls | source | 268.9 ms🏆 | — | — | — | 78.9 ms🏆 | 120.0 ms🏆 | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 881.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 892.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 894.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 892.4 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 903.7 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 7.22 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.74 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.96 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.62 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.99 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_enpls | source | — | — | — | — | 69.8 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 932.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 934.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 916.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 949.5 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 931.0 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.97 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 7.19 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.47 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.59 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.21 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.82 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_enpls | source | — | — | — | — | 58.2 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)