# `bipls_select` — biPLS — Backward Interval PLS
_Group_: **Variable selector** · _Registry tolerance_: `0.7`
## Description
biPLS backward interval elimination (§18 Phase 5p)
From the `pls4all.sklearn.BiPLSSelector` docstring:
> biPLS — backward interval elimination (Nørgaard 2000).
> **Registry note** — R `mdatools::ipls(method='backward')`. Mask RMSE-rel ~0=perfect, ~1=half disagree, ~1.41=disjoint; tolerance 0.7 enforces ~50% overlap. Backward elimination is order-sensitive.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `interval_width` | `int` | `10` | Width (in variables) of each contiguous spectral interval. |
| `min_intervals` | `int` | `2` | Minimum number of intervals retained by biPLS backward elimination. |
| `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. |
## Explanations
### Bibliographic source
Leardi, R. & Nørgaard, L. (2004). *Sequential application of backward interval partial least squares and genetic algorithms for the selection of relevant spectral regions*. Journal of Chemometrics 18(11), 486–497.
### Mathematical principle
Start with the spectrum partitioned into $I$ equal intervals (typically 10–40). At each iteration, remove the interval whose removal **least** hurts CV-RMSE — i.e. the least informative interval. Iterate until removing any further interval materially worsens performance.
Returns a multi-band subset with each band aligned to the original equal-partition grid. The discrete structure makes biPLS robust to noise (no fine-grained fishing) and easy to interpret (each retained interval is a spectroscopic region of contiguous wavelengths).
Commonly chained with GA-PLS as a coarse-to-fine pipeline (Leardi & Nørgaard 2004): biPLS narrows the candidate intervals, GA-PLS does the within-interval feature selection.
### Implementation
`n4m_bipls_select`. Reference: R `plsVarSel`.
### 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_bipls_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 bipls_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = bipls_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 BiPLSSelector
mdl = BiPLSSelector(n_components=2, interval_width=10, min_intervals=2, 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("bipls_select", X, y,
n_components = 4L, params = list(interval_width = 5L, min_intervals = 2L))
# 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.bipls_select(X, y, 4);
% see header of bindings/matlab/+pls4all/bipls_select.m for full
% parameter surface:
% res = bipls_select(X, Y, n_components, interval_width, min_intervals)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("bipls_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_mdatools`** (R · r) — `mdatools` 0.15.0 · qualitative (rmse_rel ≤ 7e-01) — R `mdatools::ipls(method='backward')` — biPLS elimination. Returns variables from intervals that survive the backward sweep.
:::
### 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 ≤ 7e-01` 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 | ≈ +8e-01 | 118.4 ms | 4.94 ms | 2.6 s🏆 | 501.6 s🏆 | 3.39 ms🏆 | 6.88 ms🏆 | 22.6 ms | 19.4 s🏆 | — | 168.7 ms | 235.7 s | — | 1.0 s | — |
pls4all.cpp.blas+omp | ≈ +8e-01 | 115.9 ms | 5.12 ms | 2.8 s | 526.0 s | 3.48 ms | 7.25 ms | 21.9 ms🏆 | 20.3 s | — | 161.9 ms🏆 | 214.9 s🏆 | — | 1.0 s🏆 | — |
pls4all.cpp.omp | ≈ +8e-01 | 154.9 ms | 4.30 ms🏆 | 3.9 s | 850.2 s | 4.03 ms | 10.2 ms | 26.1 ms | 27.1 s | — | 189.1 ms | 317.3 s | — | 1.2 s | — |
pls4all.cpp.ref | ≈ +8e-01 | 160.8 ms | 6.25 ms | 4.0 s | 666.2 s | 4.07 ms | 11.3 ms | 27.9 ms | 27.3 s | — | 186.9 ms | 320.3 s | — | 1.3 s | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 113.9 ms🏆 | — | — | — | 3.53 ms | 7.51 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | 116.7 ms | — | — | — | 4.08 ms | 7.45 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 164.3 ms | — | — | — | 8.46 ms | 18.5 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 170.2 ms | — | — | — | 12.5 ms | 17.9 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 178.0 ms | — | — | — | 8.97 ms | 14.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 172.0 ms | — | — | — | 9.71 ms | 13.8 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✓ bind | 144.4 ms | — | — | — | 4.93 ms | 11.5 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✓ bind | 125.7 ms | — | — | — | 6.08 ms | 9.40 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | 17.3 s | — | — | — | 313.9 ms | 467.3 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 | — | — | — | — | 3.47 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape | — | — | — | — | 3.60 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape | — | — | — | — | 5.38 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape | — | — | — | — | 3.95 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 3.70 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 3.75 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 7.62 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 8.66 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 8.41 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 9.23 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✓ bind | — | — | — | — | 4.60 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✓ bind | — | — | — | — | 4.88 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | — | — | — | — | 271.3 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 | — | — | — | — | 3.13 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape | — | — | — | — | 3.22 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape | — | — | — | — | 3.61 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape | — | — | — | — | 3.69 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 3.19 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 3.25 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 6.01 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 7.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 7.07 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 7.59 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✓ bind | — | — | — | — | 4.08 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✓ bind | — | — | — | — | 4.36 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | — | — | — | — | 244.9 ms | — | — | — | — | — | — | — | — | — |
:::
::::
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_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)