# `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_feature_selection_cars_select`. Reference: R `enpls 6.1.1` (`enpls.fs(method='mc')` is the closest analogue). R roxygen note (`selectors.R::cars_select`): > CARS — Competitive Adaptive Reweighted Sampling. 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_feature_selection_cars_select(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} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- cars_select(X, Y, n_components, n_iterations = 50L, min_features = 5L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{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  ·  ⇄ 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`](../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
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00780.7 ms
Python · pls4all
pls4all.python✓ J 1.00772.6 ms
R · pls4all
pls4all.R⇄ J 0.2913.3 ms
pls4all.R.formula⇄ J 0.2910.2 ms🏆
pls4all.R.mdatools⇄ J 0.2916.4 ms
pls4all.R.pls⇄ J 0.2913.3 ms
R · external
📐ref.r_enplssource188.9 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00767.0 ms
Python · pls4all
pls4all.python✓ J 1.00761.2 ms
R · pls4all
pls4all.R⇄ J 0.295.13 ms🏆
pls4all.R.formula⇄ J 0.295.78 ms
pls4all.R.mdatools⇄ J 0.295.88 ms
pls4all.R.pls⇄ J 0.295.70 ms
R · external
📐ref.r_enplssource62.9 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00881.2 ms
Python · pls4all
pls4all.python✓ J 1.00802.5 ms
R · pls4all
pls4all.R⇄ J 0.294.98 ms🏆
pls4all.R.formula⇄ J 0.295.70 ms
pls4all.R.mdatools⇄ J 0.295.89 ms
pls4all.R.pls⇄ J 0.295.76 ms
R · external
📐ref.r_enplssource63.6 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)