# `ipw_select` — IPW — Iterative Predictor Weighting
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
IPW-PLS iterative predictor weighting (§18 Phase 5t)
From the `pls4all.sklearn.IPWSelector` docstring:
> Iterative Predictor Weighting PLS selector.
> **Registry note** — R `plsVarSel::ipw_pls` iterative predictor weighting (RC filter, scale=TRUE, no.iter=3, IPW.threshold=0.01). Default `_ipw_select_pls4all` path mirrors the same R call with seed=11, giving bit-exact mask parity. The C++ top-k iterative-score 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` | `20` | Number of selection iterations or Monte-Carlo passes. |
| `damping` | `float` | `0.5` | Exponential moving-average factor mixing previous and current weights in IPW. |
| `weight_floor` | `float` | `1e-06` | Lower bound applied to per-feature weights to prevent zero-trapping. |
| `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
Forina, M., Casolino, C. & Pizarro Millán, C. (1999). *Iterative predictor weighting (IPW) PLS: a technique for the elimination of useless predictors in regression problems*. Journal of Chemometrics 13(2), 165–184. https://doi.org/10.1002/(SICI)1099-128X(199903/04)13:2<165::AID-CEM535>3.0.CO;2-Y
### Mathematical principle
IPW iteratively re-weights features in $\mathbf{X}$ by their importance, refits PLS on the re-weighted data, and tracks the score path. Weights are derived from coefficient magnitude after each fit; the iteration converges to a stable importance ranking.
Compared to single-fit coefficient ranking, IPW's iterative refinement gives more stable rankings when the calibration set is small or noisy. Exposes both the score path (for diagnostic) and the weight path (for interpretation).
### Implementation
`n4m_ipw_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_ipw_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 ipw_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = ipw_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 IPWSelector
mdl = IPWSelector(top_k, n_components=2, n_iterations=20, damping=0.5, weight_floor=1e-06, 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("ipw_select", X, y,
n_components = 4L, params = list(n_iterations = 5L, top_k = 4L, damping = 0.5, weight_floor = 0.01))
# 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.ipw_select(X, y, 4);
% see header of bindings/matlab/+pls4all/ipw_select.m for full
% parameter surface:
% res = ipw_select(X, Y, n_components, n_iterations, top_k, damping, weight_floor)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("ipw_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::ipw_pls` — iterative predictor weighting with the RC 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 | ≈ | 463.3 ms | 6.9 s🏆 | 9.2 s | 18.9 s | 490.1 ms | 429.0 ms | 7.1 s | 19.1 s | 71.3 s | 9.9 s | 67.4 s🏆 | 446.1 s | 31.0 s | 380.9 s🏆 |
pls4all.cpp.blas+omp | ≈ | 471.9 ms | 7.0 s | 8.5 s🏆 | 19.1 s | 501.2 ms | 425.9 ms | 7.5 s | 18.9 s | 69.8 s | 9.1 s🏆 | 72.4 s | 445.4 s | 30.5 s | 417.6 s |
pls4all.cpp.omp | ≈ | 479.0 ms | 7.1 s | 9.0 s | 19.4 s | 489.4 ms | 418.4 ms | 7.0 s🏆 | 19.0 s | 69.4 s | 10.6 s | 72.3 s | 444.8 s🏆 | 30.7 s | 417.8 s |
pls4all.cpp.ref | ≈ | 466.1 ms | 7.1 s | 9.4 s | 18.6 s🏆 | 497.3 ms | 418.9 ms | 7.4 s | 18.0 s🏆 | 66.3 s🏆 | 10.4 s | 72.7 s | 445.8 s | 29.6 s🏆 | 426.6 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 482.1 ms | — | — | — | 479.5 ms | 431.3 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 2.88 ms | — | — | — | 2.17 ms | 2.83 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 13.0 ms | — | — | — | 5.68 ms | 11.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 20.9 ms | — | — | — | 7.99 ms | 8.91 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 19.4 ms | — | — | — | 7.10 ms | 9.75 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 20.5 ms | — | — | — | 8.82 ms | 8.70 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.08 ms | — | — | — | 2.85 ms | 4.35 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 4.60 ms | — | — | — | 3.32 ms | 5.04 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 37.7 ms🏆 | — | — | — | 25.0 ms🏆 | 26.6 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 | — | — | — | — | 444.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 457.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 444.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 444.0 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 440.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.55 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 6.16 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.44 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.56 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.51 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.43 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 24.5 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 | — | — | — | — | 389.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 397.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 394.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 387.7 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 395.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.81 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.00 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.11 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 5.05 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.18 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.49 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.83 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 20.3 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)