# `variable_select_coef` — Coefficient-magnitude selection
_Group_: **Variable selector** · _Registry tolerance_: `1.1`
## Description
|Coef| top-k selection (§18 Phase 5a, method=1)
From the `pls4all.sklearn.CoefficientSelector` docstring:
> |coef| top-k selector. Ranks features by the magnitude of their
PLS regression coefficient on Y.
> **Registry note** — R `pls::plsr(method='simpls')` |coef| ranking. The solver mismatch is fixed, but residual top-k drift remains because pls4all ranks its stored C-kernel coefficient vector while R reconstructs coefficients through `pls`'s SIMPLS convention. Mask RMSE-rel ~0=perfect, ~1=half disagree, ~1.41=disjoint; tolerance accepts this known coefficient-convention divergence.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `top_k` | `int` | `None` | Number of features to retain. |
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `solver` | `str` | `'simpls'` | Inner algorithm: 'nipals', 'simpls', 'svd', 'kernel', 'orthogonal-scores', 'power', 'randomized-svd', 'wide-kernel'. |
| `center_x` | `bool` | `True` | Subtract the column mean of X before fitting. |
| `scale_x` | `bool` | `True` | Standardize X columns to unit variance before fitting. |
| `tol` | `float` | `1e-06` | Convergence tolerance for iterative solvers (NIPALS / power-iteration). |
| `max_iter` | `int` | `500` | Maximum iterations for iterative solvers. |
## Explanations
### Bibliographic source
Martens, H. & Næs, T. (1989). *Multivariate Calibration*, §5. — the simplest ranking baseline.
### Mathematical principle
Rank features by the absolute magnitude of their PLS regression coefficient $|b_j|$ in the original feature scale. Pick the top-$k$ as the selected subset.
This is the simplest possible PLS variable selector. It is biased — features with large variance get smaller coefficients for the same predictive effect — so it should usually be applied after autoscaling to remove the variance-induced bias. Once autoscaled, $|b_j|$ ranks features by their **standardised partial effect on $y$**, which is statistically meaningful.
Useful as a sanity-check baseline against more sophisticated selectors. If a complex method does not beat coefficient-magnitude selection, it is probably over-engineered.
### Implementation
`n4m_variable_select_rank` with metric=COEF.
MATLAB header (`bindings/matlab/+pls4all/coefficient_select.m`):
```text
pls4all.coefficient_select Coefficient-magnitude feature ranking.
res = pls4all.coefficient_select(X, Y, n_components, top_k)
Fits an internal SIMPLS model and ranks features by the magnitude of
their regression coefficients.
```
### 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_variable_select_rank(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 variable_select_rank
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = variable_select_rank(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 CoefficientSelector
mdl = CoefficientSelector(top_k, n_components=2, solver='simpls', center_x=True, scale_x=True, tol=1e-06, max_iter=500)
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("variable_select_coef", X, y,
n_components = 4L, params = list(top_k = 10L))
# 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.coefficient_select(X, y, 4);
% see header of bindings/matlab/+pls4all/coefficient_select.m for full
% parameter surface:
% res = coefficient_select(X, Y, n_components, top_k)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("variable_select_coef", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_pls`** (R · r) — `pls` 2.8.5 · qualitative (rmse_rel ≤ 1e+00) — R `pls::plsr` coefficient magnitudes — top-k indices ranked by |coef|. Mirrors method=1 of pls4all's ranker.
:::
### 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**: qualitative — shape/smoke comparison only. The external library and pls4all do not produce numerically equivalent output for this method (see the MethodSpec notes); the `rmse_rel_tol ≤ 1e+00` budget is set wide on purpose. Treat ~ shape as *“we ran both, both finished”*, not as numerical agreement.
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 | ≈ | 2.75 ms | 2.39 ms | 13.7 ms | 64.6 ms | 1.66 ms | 2.97 ms | 6.99 ms | 63.8 ms | 310.1 ms | 31.8 ms🏆 | 323.5 ms | 1.6 s🏆 | 121.7 ms🏆 | 1.3 s🏆 |
pls4all.cpp.blas+omp | ≈ | 2.77 ms | 1.95 ms🏆 | 11.9 ms🏆 | 62.2 ms🏆 | 1.57 ms🏆 | 2.63 ms🏆 | 6.91 ms | 60.2 ms🏆 | 321.5 ms | 32.1 ms | 326.3 ms | 1.6 s | 136.3 ms | 1.3 s |
pls4all.cpp.omp | ≈ | 2.53 ms🏆 | 2.20 ms | 13.0 ms | 63.9 ms | 1.76 ms | 3.17 ms | 6.57 ms🏆 | 64.7 ms | 302.3 ms🏆 | 33.8 ms | 322.3 ms | 1.6 s | 132.3 ms | 1.3 s |
pls4all.cpp.ref | ≈ | 2.59 ms | 2.46 ms | 14.4 ms | 67.1 ms | 1.59 ms | 4.04 ms | 7.27 ms | 62.3 ms | 321.1 ms | 32.6 ms | 313.0 ms🏆 | 1.6 s | 128.1 ms | 1.3 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.96 ms | — | — | — | 2.68 ms | 2.98 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | 4.48 ms | — | — | — | 2.16 ms | 3.38 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 22.5 ms | — | — | — | 5.77 ms | 15.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 28.4 ms | — | — | — | 6.59 ms | 16.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 26.0 ms | — | — | — | 5.93 ms | 10.7 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 26.8 ms | — | — | — | 8.13 ms | 15.6 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.84 ms | — | — | — | 3.12 ms | 4.48 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 5.70 ms | — | — | — | 3.37 ms | 6.07 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_pls | source | 20.8 ms | — | — | — | 17.6 ms | 23.3 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 | ~ shape | — | — | — | — | 1.57 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape | — | — | — | — | 2.37 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape | — | — | — | — | 1.63 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape | — | — | — | — | 1.55 ms🏆 | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 1.94 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 5.22 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 6.53 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 6.41 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 6.27 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.15 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 4.90 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_pls | source | — | — | — | — | 12.9 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 | ~ shape | — | — | — | — | 1.46 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape | — | — | — | — | 1.43 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape | — | — | — | — | 1.45 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape | — | — | — | — | 1.44 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.30 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 1.58 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 4.16 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 5.04 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 4.64 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 4.79 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.39 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.66 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_pls | source | — | — | — | — | 10.4 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)