bve_select — BVE — Backward Variable Elimination

Group: Variable selector · Registry tolerance: 1e-06

Description

Backward Variable Elimination (§18 Phase 5k)

From the pls4all.sklearn.BVESelector docstring:

Backward Variable Elimination with VIP filter.

Registry note — R plsVarSel::bve_pls backward elimination with VIP cut (Mehmood et al.). Default _bve_select_pls4all path mirrors the same R call with seed=11, giving bit-exact mask parity. The C++ greedy step-count RMSE backward-elimination kernel is opt-in via legacy=True.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

n_steps

int

10

Number of elimination passes performed.

min_features

`int

None`

None

n_folds

int

3

Number of cross-validation folds used inside the selector.

Explanations

Bibliographic source

Forina, M., Casolino, M. C. & Pizarro Millán, C. (2004). Iterative predictor weighting (IPW) PLS: a technique for the elimination of useless predictors in regression problems. Journal of Chemometrics 18(2), 105–112 (§2).

Mathematical principle

Greedy backward elimination: at each step, evaluate every possible one-variable removal by CV-RMSE and drop the feature whose removal hurts least (or helps most). Continue until either a target subset size is reached or removal starts to hurt CV-RMSE materially.

Cost: \(O(p^2 \cdot \mathrm{CV})\) — quadratic in the number of features, since each step evaluates \(\sim p\) candidate removals. For \(p \le 200\) this is tractable; for larger spectra the shaving variant is preferred.

Strength: BVE is essentially exhaustive at each step, so it cannot be tricked by collinearity the way SPA can. Weakness: very expensive on full NIR spectra.

Implementation

n4m_bve_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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_bve_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);

import pls4all
from pls4all._methods import bve_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = bve_select_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import BVESelector
mdl = BVESelector(n_components=2, n_steps=10, min_features=None, n_folds=3)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("bve_select", X, y,
                      n_components = 4L, params = list(n_steps = 35L, min_features = 5L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.bve_select(X, y, 4);
% see header of bindings/matlab/+pls4all/bve_select.m for full
% parameter surface:
%   res = bve_select(X, Y, n_components, n_steps, min_features)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("bve_select", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 ref.r_plsvarsel (R · r) — plsVarSel 0.10.0 · strict (rmse_rel ≤ 1e-06) — R plsVarSel::bve_pls — backward variable elimination with VIP filter.

Benchmarks

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 = 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). 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.

BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00510.0 ms
Python · pls4all
pls4all.python✓ J 1.00563.8 ms
pls4all.sklearn⇄ J 0.4042.4 ms🏆
R · pls4all
pls4all.R⇄ J 0.4058.7 ms
pls4all.R.formula⇄ J 0.4066.5 ms
pls4all.R.mdatools⇄ J 0.40152.1 ms
pls4all.R.pls⇄ J 0.40141.0 ms
R · external
📐ref.r_plsvarselsource46.9 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00491.1 ms
Python · pls4all
pls4all.python✓ J 1.00491.1 ms
pls4all.sklearn⇄ J 0.4043.0 ms🏆
R · pls4all
pls4all.R⇄ J 0.4061.4 ms
pls4all.R.formula⇄ J 0.4062.6 ms
pls4all.R.mdatools⇄ J 0.4062.1 ms
pls4all.R.pls⇄ J 0.4061.3 ms
R · external
📐ref.r_plsvarselsource47.3 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00507.2 ms
Python · pls4all
pls4all.python✓ J 1.00479.8 ms
pls4all.sklearn⇄ J 0.4043.9 ms🏆
R · pls4all
pls4all.R⇄ J 0.4061.3 ms
pls4all.R.formula⇄ J 0.4062.1 ms
pls4all.R.mdatools⇄ J 0.40109.1 ms
pls4all.R.pls⇄ J 0.4060.9 ms
R · external
📐ref.r_plsvarselsource45.8 ms

See also: benchmark overview · methods index · interactive dashboard