# `irf_select` — IRF — Iterative Random Forest
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
Interval Random Frog (Phase 52)
From the `pls4all.sklearn.IRFSelector` docstring:
> IRF — Interval Random Frog (Yun 2013).
> **Registry note** — Python `auswahl.IntervalRandomFrog` (LSX-UniWue; Yun 2013). Same algorithm as libPLS `irf`. Default `_irf_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. |
| `window_size` | `int` | `5` | Length of the moving window for recursive / interval-random-frog models. |
| `initial_intervals` | `int` | `5` | Number of seed intervals for the interval-random-frog walk. |
| `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. |
## Explanations
### Bibliographic source
Basu, S., Kumbier, K., Brown, J. B. & Yu, B. (2018). *Iterative random forests to discover predictive and stable high-order interactions*. Proceedings of the National Academy of Sciences 115(8), 1943–1948.
### Mathematical principle
IRF iteratively re-weights random forest feature importances and refits. At each iteration, features with high feature-importance get oversampled in the bootstrap of the next forest; the loop converges to a stable ranking of features by their **interaction-aware** importance.
Adapted for PLS prediction: the IRF importance ranking is used to select the top-$k$ features, then PLS is fit on the selected subset. The RF importance is non-linear so this catches predictive features that interact rather than contributing additively — typically missed by linear selectors like VIP.
### Implementation
`n4m_irf_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_irf_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 irf_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = irf_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 IRFSelector
mdl = IRFSelector(top_k, n_components=2, n_iterations=100, window_size=5, initial_intervals=5, 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("irf_select", X, y,
n_components = 3L, params = list(n_iterations = 30L, window_size = 4L, initial_intervals = 5L, top_k = 5L, 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("irf_select", X, y, "NumComponents", 3);
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("irf_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.IntervalRandomFrog` (LSX-UniWue; Yun 2013). Same algorithm as libPLS `irf` 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) | 120×30 (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 | ≈ | 247.6 ms | 2.5 s | 2.6 s🏆 | 3.6 s | 140.1 ms | 188.8 ms🏆 | 4.4 s🏆 | 4.3 s🏆 | 5.5 s | 7.5 s | 6.2 s | 12.7 s | 19.0 s | 23.1 s |
pls4all.cpp.blas+omp | ≈ | 236.0 ms🏆 | 2.5 s | 3.0 s | 3.8 s | 146.2 ms | 200.0 ms | 5.0 s | 4.7 s | 5.2 s🏆 | 7.6 s | 6.6 s | 11.8 s | 18.4 s🏆 | 21.1 s |
pls4all.cpp.omp | ≈ | 241.1 ms | 2.4 s | 3.1 s | 2.9 s🏆 | 146.1 ms | 196.5 ms | 5.0 s | 4.4 s | 5.5 s | 7.2 s🏆 | 5.8 s | 11.0 s🏆 | 18.7 s | 20.9 s🏆 |
pls4all.cpp.ref | ≈ | 237.6 ms | 2.1 s🏆 | 3.0 s | 4.0 s | 137.3 ms | 209.2 ms | 5.3 s | 4.4 s | 5.8 s | 7.8 s | 5.6 s🏆 | 11.4 s | 19.5 s | 23.7 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 245.3 ms | — | — | — | 140.3 ms | 192.8 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 3.72 ms | — | — | — | 1.88 ms | 6.18 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 11.1 ms | — | — | — | 3.39 ms | 12.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 20.9 ms | — | — | — | 6.08 ms | 13.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 21.6 ms | — | — | — | 4.91 ms | 12.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 21.9 ms | — | — | — | 4.67 ms | 13.5 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.27 ms | — | — | — | 2.09 ms | 9.46 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 5.68 ms | — | — | — | 2.77 ms | 14.5 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | 238.0 ms | — | — | — | 129.1 ms🏆 | 191.1 ms | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 120×30 (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 | — | — | — | — | 114.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 118.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 111.4 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 113.3 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 127.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.73 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.17 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 4.35 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 4.55 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 4.34 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.48 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | — | — | — | — | 122.7 ms | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 120×30 (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 | — | — | — | — | 108.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 110.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 106.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 114.8 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 114.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.60 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 2.69 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 3.59 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 3.52 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 3.65 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 1.84 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.19 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | — | — | — | — | 103.8 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)