# `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` | 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. |
## 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**
::::{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_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);
```
:::
:::{tab-item} Python · pls4all (raw)
:sync: python-raw
:class-label: lang-python
```python
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"), …
```
:::
:::{tab-item} Python · pls4all.sklearn
:sync: python-sklearn
:class-label: lang-python
```python
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)
```
:::
:::{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("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.
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
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);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("bve_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::bve_pls` — backward variable elimination with VIP filter.
:::
### 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
| 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 | ✗ +6e-01 | 508.7 ms | 3.0 s | 4.0 s🏆 | 10.8 s | 563.4 ms | 548.8 ms | 4.4 s🏆 | 27.7 s | 145.8 s | 24.5 s | 347.9 s | — | — | — |
pls4all.cpp.blas+omp | ✗ +6e-01 | 507.8 ms | 3.2 s | 4.3 s | 10.5 s | 568.5 ms | 537.2 ms | 4.5 s | 27.1 s | 152.3 s | 25.2 s | 340.2 s | — | — | — |
pls4all.cpp.omp | ✗ +6e-01 | 502.2 ms | 3.1 s | 4.4 s | 10.1 s | 562.6 ms | 544.8 ms | 4.6 s | 27.6 s | 149.9 s | 24.0 s | 336.4 s | — | — | — |
pls4all.cpp.ref | ✗ +6e-01 | 526.8 ms | 3.0 s | 4.4 s | 9.7 s🏆 | 566.9 ms | 546.9 ms | 4.7 s | 27.0 s🏆 | 140.5 s🏆 | 23.0 s🏆 | 330.8 s🏆 | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 490.7 ms | — | — | — | 572.0 ms | 538.6 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 2.0 s | — | — | — | 51.2 ms | 93.2 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 11.1 ms | — | — | — | 5.98 ms | 11.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 21.0 ms | — | — | — | 7.18 ms | 8.98 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 21.0 ms | — | — | — | 7.16 ms | 9.07 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 21.0 ms | — | — | — | 7.33 ms | 10.8 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 2.6 s | — | — | — | 52.0 ms | 97.6 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 2.5 s | — | — | — | 49.3 ms | 109.0 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 45.7 ms🏆 | — | — | — | 53.9 ms🏆 | 132.8 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 | — | — | — | — | 510.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 503.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 505.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 513.1 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 480.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 42.8 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.52 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.49 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.64 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.29 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 45.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 45.3 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 47.5 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 | — | — | — | — | 422.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 425.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 421.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 418.1 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 423.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 40.9 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.36 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.30 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 5.04 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.29 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 41.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 42.7 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 45.7 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
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_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)