# `random_frog_select` — Random Frog
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
Random Frog selection (§18 Phase 5g)
From the `pls4all.sklearn.RandomFrogSelector` docstring:
> Random Frog feature selection (Li 2012).
> **Registry note** — Python `auswahl.RandomFrog` (LSX-UniWue; Li 2012). Same algorithm as libPLS `randomfrog_pls`. Default `_random_frog_select_pls4all` path mirrors the same auswahl call with `random_state=seed`, giving bit-exact mask parity. The C++ splitmix64 kernel is opt-in via `legacy=True`.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `top_k` | `int` | `None` | Number of features to retain. |
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `n_iterations` | `int` | `100` | Number of selection iterations or Monte-Carlo passes. |
| `initial_size` | `int` | `20` | Starting subset size for the random-frog chain. |
| `min_size` | `int | None` | `None` | Minimum allowed subset size during the random-frog Markov chain. |
| `max_size` | `int | None` | `None` | Maximum allowed subset size during the random-frog Markov chain. |
| `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
Li, H., Xu, Q. & Liang, Y. (2012). *Random frog: an efficient reversible jump Markov chain Monte Carlo-like approach for variable selection*. Analytica Chimica Acta 740, 20–26.
### Mathematical principle
Random Frog runs a random walk over feature subsets: at each step it proposes a transition to a neighbouring subset (add / remove / swap a feature) and accepts the transition with a Metropolis-style probability based on the improvement in CV-RMSE. Features that appear frequently in the visited subsets are deemed important.
Output: the **inclusion frequency** vector — fraction of iterations in which each feature was selected. Sort by frequency and take the top-$k$ for the final subset.
Random Frog is sample-efficient compared to GA-PLS (no population of full subsets to maintain) but slower to mix on very high-dimensional data. Recommended on spectra of moderate size (a few hundred wavelengths).
### Implementation
`n4m_random_frog_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_random_frog_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 random_frog_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = random_frog_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 RandomFrogSelector
mdl = RandomFrogSelector(top_k, n_components=2, n_iterations=100, initial_size=20, min_size=None, max_size=None, 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("random_frog_select", X, y,
n_components = 4L, params = list(n_iterations = 10L, initial_size = 10L, min_size = 5L, max_size = 20L, top_k = 10L, seed = 11L))
# 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.fit("random_frog_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("random_frog_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_auswahl`** (python · python) — `auswahl` 0.9.0 · strict (rmse_rel ≤ 1e-06) — Python `auswahl.RandomFrog` (LSX-UniWue; Li 2012). Same algorithm as libPLS `randomfrog_pls` with pinned `random_state` for bit-exact mask parity.
:::
### 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 | ≈ | 114.7 ms | 641.7 ms | 776.9 ms | 662.0 ms | 101.4 ms | 123.2 ms | 600.8 ms🏆 | 943.7 ms | 1.2 s🏆 | 1.3 s | 1.9 s | 5.5 s | 4.4 s | 5.2 s🏆 |
pls4all.cpp.blas+omp | ≈ | 108.3 ms | 788.3 ms | 560.7 ms | 630.2 ms | 95.3 ms🏆 | 114.9 ms🏆 | 692.6 ms | 959.6 ms | 1.4 s | 1.0 s🏆 | 1.9 s | 5.1 s | 3.5 s🏆 | 6.0 s |
pls4all.cpp.omp | ≈ | 111.5 ms | 754.3 ms | 655.7 ms | 589.4 ms🏆 | 108.6 ms | 122.6 ms | 619.1 ms | 865.1 ms | 1.4 s | 1.1 s | 1.8 s🏆 | 4.8 s | 3.6 s | 5.2 s |
pls4all.cpp.ref | ≈ | 111.7 ms | 574.0 ms🏆 | 355.4 ms🏆 | 842.8 ms | 101.5 ms | 127.2 ms | 772.7 ms | 840.3 ms🏆 | 1.4 s | 1.1 s | 1.9 s | 4.7 s🏆 | 4.0 s | 5.8 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 116.4 ms | — | — | — | 100.6 ms | 124.6 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 3.17 ms | — | — | — | 2.44 ms | 3.49 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 11.7 ms | — | — | — | 7.06 ms | 10.9 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 21.9 ms | — | — | — | 7.36 ms | 13.9 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 21.4 ms | — | — | — | 7.19 ms | 11.1 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 19.8 ms | — | — | — | 7.48 ms | 9.94 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 6.27 ms | — | — | — | 3.41 ms | 5.59 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 5.23 ms | — | — | — | 3.87 ms | 5.78 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | 104.9 ms🏆 | — | — | — | 101.4 ms | 120.7 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 | — | — | — | — | 77.1 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 79.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 79.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 79.1 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 79.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.42 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.82 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.91 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.62 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.83 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.00 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.85 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | — | — | — | — | 87.2 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 | — | — | — | — | 74.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 75.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 73.4 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 73.9 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 74.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.65 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.61 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.31 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 5.51 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.53 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.80 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.21 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | — | — | — | — | 75.2 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)