# `rep_select` — REP — Recursive Elimination of Predictors
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
REP-PLS repeated VIP selection (§18 Phase 5s)
From the `pls4all.sklearn.REPSelector` docstring:
> REP-PLS — repeated VIP-thresholded variable selection.
> **Registry note** — R `plsVarSel::rep_pls` repeated VIP-filtered selection. Default `_rep_select_pls4all` path mirrors the same R call with seed=11, giving bit-exact mask parity. The C++ step-count 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`). |
| `remove_count` | `int` | `1` | Number of variables removed per REP step. |
| `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. |
| `rep_ratio` | `float` | `0.5` | registry benchmark cell value |
| `rep_vip_threshold` | `float` | `0.5` | registry benchmark cell value |
| `rep_repeats` | `int` | `3` | registry benchmark cell value |
## Explanations
### Bibliographic source
Mehmood, T., Liland, K. H., Snipen, L. & Sæbø, S. (2012). *A review of variable selection methods in partial least squares regression*. Chemometrics and Intelligent Laboratory Systems 118, 62–69. https://doi.org/10.1016/j.chemolab.2012.07.010 — same review as `shaving_select`; §3.3 *Recursive elimination* introduces the fixed-count variant implemented here.
### Mathematical principle
REP removes a **fixed count** of features per recursive step (rather than a fraction as in shaving). At each step, sort features by absolute coefficient score, remove the $m$ lowest, refit, record CV-RMSE. Return the subset with lowest CV-RMSE across all retained trajectories.
Useful when the analyst wants control over total iteration count: with $m$ features removed per step, the process terminates in $\lceil p / m \rceil$ iterations. Same intent as shaving but with linear instead of geometric decay.
### Implementation
`n4m_rep_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_rep_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 rep_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = rep_select_fit(ctx, cfg, X, y, n_components=3)
# 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 REPSelector
mdl = REPSelector(n_components=2, n_steps=10, min_features=None, remove_count=1, 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("rep_select", X, y,
n_components = 3L, params = list(n_steps = 9L, min_features = 6L, remove_count = 5L, rep_ratio = 0.5, rep_vip_threshold = 0.5, rep_repeats = 3L))
# 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.rep_select(X, y, 3);
% see header of bindings/matlab/+pls4all/rep_select.m for full
% parameter surface:
% res = rep_select(X, Y, n_components, n_steps, min_features, remove_count)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("rep_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::rep_pls` — repeated VIP-thresholded variable selection.
:::
### 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 | ≈ | 1.4 s | 7.2 s | 53.9 s | 760.9 s | 801.6 ms | 763.9 ms | 9.7 s | 547.7 s | — | 53.0 s🏆 | — | — | — | — |
pls4all.cpp.blas+omp | ≈ | 1.3 s | 6.8 s🏆 | 54.5 s | 729.0 s🏆 | 816.3 ms | 776.4 ms | 8.9 s🏆 | 541.0 s | — | 55.7 s | — | — | — | — |
pls4all.cpp.omp | ≈ | 1.3 s | 7.1 s | 48.0 s🏆 | 735.8 s | 784.0 ms | 768.7 ms | 9.3 s | 534.0 s🏆 | — | 58.7 s | — | — | — | — |
pls4all.cpp.ref | ≈ | 1.4 s | 7.4 s | 55.1 s | 748.9 s | 798.7 ms | 786.8 ms | 9.7 s | 537.1 s | — | 54.9 s | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 1.3 s | — | — | — | 817.3 ms | 773.9 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 4.06 ms | — | — | — | 4.10 ms | 4.06 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 13.5 ms | — | — | — | 6.31 ms | 11.1 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 24.3 ms | — | — | — | 10.0 ms | 12.6 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 21.2 ms | — | — | — | 8.36 ms | 9.68 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 23.9 ms | — | — | — | 8.51 ms | 13.1 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.98 ms | — | — | — | 3.30 ms | 7.83 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 6.89 ms | — | — | — | 4.05 ms | 8.05 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 930.6 ms🏆 | — | — | — | 283.8 ms🏆 | 293.2 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 | — | — | — | — | 723.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 731.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 720.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 717.9 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 726.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.57 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 6.16 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 7.18 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.95 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 7.53 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.16 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.68 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 254.1 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 | — | — | — | — | 612.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 616.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 611.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 606.9 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 620.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.19 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.73 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.23 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 5.38 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.68 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.86 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.22 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 223.7 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)