# `scars_select` — SCARS — Stability-CARS _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description SCARS stability + CARS (§18 Phase 5h) From the `pls4all.sklearn.SCARSSelector` docstring: > Stability-CARS hybrid (Zheng 2014). > **Registry note** — NumPy port of Stability CARS (Zheng 2014) — Monte-Carlo subsampling + stability scoring + CARS exponential shrinkage. Default `_scars_select_pls4all` path invokes the same NumPy function with `np.random.default_rng(seed)`, giving bit-exact mask parity. The C++ splitmix64 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`). | | `sample_fraction` | `float` | `0.8` | Fraction of samples drawn per Monte-Carlo replicate. | | `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. | | `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. | ## Explanations ### Bibliographic source Zheng, K., Li, Q., Wang, J., Geng, J., Cao, P., Sui, T., Wang, X. & Du, Y. (2012). *Stability competitive adaptive reweighted sampling (SCARS) and its applications to multivariate calibration of NIR spectra*. Chemometrics and Intelligent Laboratory Systems 112, 48–54. ### Mathematical principle Replace CARS's coefficient-magnitude weights with **coefficient-stability** weights: $w_j = |\bar{b}_j| / s(b_j)$ from the bootstrap distribution. Stability-weighted retention is more robust to spurious high-magnitude coefficients caused by particular bootstrap subsamples. Otherwise identical to CARS: exponential decay schedule and stochastic competition. SCARS typically improves CARS on datasets with strong baseline drift or where a few high-leverage samples dominate the coefficient estimates. ### Implementation `n4m_scars_select`. ### 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_scars_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 scars_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = scars_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 SCARSSelector mdl = SCARSSelector(n_components=2, n_iterations=50, min_features=None, sample_fraction=0.8, 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("scars_select", X, y, n_components = 4L, params = list(n_iterations = 8L, min_features = 5L, sample_fraction = 0.5, seed = 11L)) # 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.fit("scars_select", X, y, "NumComponents", 4); yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("scars_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_scars_numpy_port`** (python · python) — `scars_numpy_port` 1.0.0 · strict (rmse_rel ≤ 1e-06) — NumPy port of Stability CARS (Zheng 2014) — Monte-Carlo subsampling + stability scoring + CARS exponential shrinkage. Pinned `np.random.default_rng(seed)` for bit-exact reproducibility. ::: ### 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 ≤ 1e-06`). 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
BackendParity50×250 (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≈5.88 ms🏆15.2 ms61.0 ms237.5 ms4.47 ms5.31 ms39.1 ms🏆247.4 ms1.0 s124.0 ms1.1 s5.2 s🏆449.0 ms3.7 s
pls4all.cpp.blas+omp≈6.15 ms31.5 ms59.8 ms217.3 ms🏆4.10 ms5.29 ms43.2 ms202.1 ms🏆976.7 ms111.6 ms🏆952.5 ms5.4 s423.9 ms4.1 s
pls4all.cpp.omp≈6.26 ms23.3 ms59.9 ms219.7 ms4.32 ms5.95 ms40.1 ms216.4 ms963.7 ms124.6 ms701.8 ms🏆5.7 s352.9 ms🏆3.2 s🏆
pls4all.cpp.ref≈6.18 ms13.1 ms🏆31.8 ms🏆232.3 ms3.92 ms🏆5.22 ms🏆45.8 ms256.7 ms881.5 ms🏆133.6 ms1.0 s5.6 s461.6 ms3.9 s
Python · pls4all
pls4all.python✓ bind5.94 ms———4.24 ms6.01 ms————————
pls4all.sklearn✗ +1e+003.35 ms———3.95 ms3.54 ms————————
R · pls4all
pls4all.R✗ +1e+0012.0 ms———7.23 ms11.1 ms————————
pls4all.R.formula✗ +1e+0022.6 ms———7.77 ms9.41 ms————————
pls4all.R.mdatools✗ +1e+0020.8 ms———7.59 ms11.4 ms————————
pls4all.R.pls✗ +1e+0021.6 ms———9.63 ms12.4 ms————————
MATLAB · pls4all
pls4all.matlab✗ +1e+007.30 ms———3.18 ms5.32 ms————————
pls4all.matlab.classdef✗ +1e+006.44 ms———4.12 ms6.08 ms————————
Python · external
📐ref.python_scars_numpy_portsource6.02 ms———4.76 ms5.28 ms————————
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity50×250 (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————3.95 ms—————————
pls4all.cpp.blas+omp✓ ref————4.49 ms—————————
pls4all.cpp.omp✓ ref————4.12 ms—————————
pls4all.cpp.ref✓ ref————4.03 ms—————————
Python · pls4all
pls4all.python✓ bind————3.85 ms🏆—————————
pls4all.sklearn✗ +1e+00————2.54 ms—————————
R · pls4all
pls4all.R✗ +1e+00————5.89 ms—————————
pls4all.R.formula✗ +1e+00————7.11 ms—————————
pls4all.R.mdatools✗ +1e+00————7.63 ms—————————
pls4all.R.pls✗ +1e+00————7.09 ms—————————
MATLAB · pls4all
pls4all.matlab✗ +1e+00————3.10 ms—————————
pls4all.matlab.classdef✗ +1e+00————3.55 ms—————————
Python · external
📐ref.python_scars_numpy_portsource————3.92 ms—————————
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity50×250 (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————3.73 ms—————————
pls4all.cpp.blas+omp✓ ref————4.28 ms—————————
pls4all.cpp.omp✓ ref————3.58 ms—————————
pls4all.cpp.ref✓ ref————3.58 ms🏆—————————
Python · pls4all
pls4all.python✓ bind————4.26 ms—————————
pls4all.sklearn✗ +1e+00————2.15 ms—————————
R · pls4all
pls4all.R✗ +1e+00————4.60 ms—————————
pls4all.R.formula✗ +1e+00————5.91 ms—————————
pls4all.R.mdatools✗ +1e+00————5.35 ms—————————
pls4all.R.pls✗ +1e+00————5.39 ms—————————
MATLAB · pls4all
pls4all.matlab✗ +1e+00————2.84 ms—————————
pls4all.matlab.classdef✗ +1e+00————3.17 ms—————————
Python · external
📐ref.python_scars_numpy_portsource————3.63 ms—————————
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)