# `ga_select` — GA-PLS — Genetic Algorithm variable selection _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description GA-PLS genetic algorithm selection From the `pls4all.sklearn.GASelector` docstring: > Genetic Algorithm feature selection. > **Registry note** — R `plsVarSel::ga_pls` genetic-algorithm variable selection. Default `_ga_select_pls4all` path mirrors the same R call with seed=11 (iters=5, popSize=20, GA.threshold=3), giving bit-exact mask parity. The C++ splitmix64 GA kernel is opt-in via `legacy=True`. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `n_generations` | `int` | `30` | Number of GA generations to evolve. | | `population_size` | `int` | `40` | Number of candidate feature subsets per generation. | | `min_features` | `int | None` | `None` | Minimum number of variables the selector is allowed to keep (defaults to `n_components`). | | `max_features` | `int | None` | `None` | Upper bound on the GA chromosome cardinality (defaults to all features). | | `mutation_rate` | `float` | `0.05` | Per-bit mutation probability applied to GA chromosomes. | | `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 Leardi, R. (2000). *Application of genetic algorithm–PLS for feature selection in spectral data sets*. Journal of Chemometrics 14(5–6), 643–655. ### Mathematical principle Wrap a binary genetic algorithm around PLS CV-RMSE. Each chromosome is a $p$-bit binary mask encoding which features to include; fitness is $-\mathrm{CV\text{-}RMSE}$ from PLS on the masked subset; standard GA operators (single-point crossover, bit-flip mutation, elitism) drive the population. Cost is high — every fitness evaluation is a full PLS fit — but GA-PLS handles non-convex fitness landscapes (non-additive interactions between selected features) that greedy methods miss. Recommended population sizes: 30–100; generations: 100–500. Stochastic by construction: results vary across RNG seeds. For deterministic comparisons against this selector the benchmark widens the parity tolerance and fixes the seed; in production use a small ensemble of GA runs and take the consensus. ### Implementation `n4m_feature_selection_ga_select`. Reference: R `plsVarSel`. R roxygen note (`methods_extra.R::ga_select`): > GA-PLS — genetic algorithm variable selection. > @param n_components Integer. Number of latent components. > @param n_generations Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param population_size Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param min_features Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param max_features Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param mutation_rate Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param seed Integer. Random seed for reproducibility. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export ### 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_ga_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 ga_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = ga_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 GASelector mdl = GASelector(n_components=2, n_generations=30, population_size=40, min_features=None, max_features=None, mutation_rate=0.05, 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("ga_select", X, y, n_components = 4L, params = list(n_generations = 5L, population_size = 12L, min_features = 5L, max_features = 20L, mutation_rate = 0.1, seed = 11L)) # 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 <- ga_select(X, Y, n_components, n_generations = 50L, population_size = 50L, min_features = NULL, max_features = NULL, mutation_rate = 0.01, seed = 0L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.fit("ga_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("ga_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.r_plsvarsel`** (R · r) — `plsVarSel` 0.10.0 · strict (rmse_rel ≤ 1e-06) — R `plsVarSel::ga_pls` — genetic-algorithm variable selection. RNG differs from pls4all's GA so set overlap is loose. ::: ### 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 ≤ 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
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00607.6 ms
Python · pls4all
pls4all.python✓ J 1.00756.5 ms
pls4all.sklearn⇄ J 0.323.94 ms🏆
R · pls4all
pls4all.R⇄ J 0.327.38 ms
pls4all.R.formula⇄ J 0.328.59 ms
pls4all.R.mdatools⇄ J 0.3216.0 ms
pls4all.R.pls⇄ J 0.329.76 ms
R · external
📐ref.r_plsvarselsource218.7 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00628.1 ms
Python · pls4all
pls4all.python✓ J 1.00600.8 ms
pls4all.sklearn⇄ J 0.323.94 ms🏆
R · pls4all
pls4all.R⇄ J 0.327.17 ms
pls4all.R.formula⇄ J 0.327.95 ms
pls4all.R.mdatools⇄ J 0.328.10 ms
pls4all.R.pls⇄ J 0.328.03 ms
R · external
📐ref.r_plsvarselsource425.9 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00626.6 ms
Python · pls4all
pls4all.python✓ J 1.001.8 s
pls4all.sklearn⇄ J 0.323.88 ms🏆
R · pls4all
pls4all.R⇄ J 0.327.01 ms
pls4all.R.formula⇄ J 0.327.86 ms
pls4all.R.mdatools⇄ J 0.327.57 ms
pls4all.R.pls⇄ J 0.327.89 ms
R · external
📐ref.r_plsvarselsource226.4 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)