interval_select — iPLS — Interval PLS (moving-window)

Group: Variable selector · Registry tolerance: 1e-06

Description

Interval/iPLS forward selection (§18 Phase 5b)

From the pls4all.sklearn.IntervalSelector docstring:

Forward interval PLS (iPLS, Nørgaard 2000).

Registry note — R mdatools::ipls(method='forward'). Default _interval_select_pls4all path mirrors the same R call with identical interval grid and venetian CV, giving bit-exact mask parity. The C++ contiguous-fold kernel is opt-in via legacy=True.

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.
step	int	5	Stride between consecutive forward-iPLS intervals.
n_folds	int	3	Number of cross-validation folds used inside the selector.
interval_step	int	2	registry benchmark cell value

Explanations

Bibliographic source

Nørgaard, L., Saudland, A., Wagner, J., Nielsen, J. P., Munck, L. & Engelsen, S. B. (2000). Interval partial least-squares regression (iPLS): a comparative chemometric study with an example from near-infrared spectroscopy. Applied Spectroscopy 54(3), 413–419.

Mathematical principle

Slide a fixed-width window of \(w\) consecutive wavelengths across the spectrum, fit PLS on each window alone, evaluate by CV-RMSE. The window with the lowest CV-RMSE is returned as the selected interval.

iPLS is the simplest interval selector — it returns a single contiguous band rather than scattered wavelengths. The output is therefore directly interpretable as a spectroscopic feature (functional group, electronic transition, …). For multi-band selection use biPLS or siPLS.

The window width \(w\) is the main tunable; cross-validating \(w\) jointly with the window position is the standard extension.

Implementation

n4m_interval_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

C ABI · libn4m

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_interval_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);

Python · pls4all (raw)

import pls4all
from pls4all._methods import interval_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = interval_select_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

Python · pls4all.sklearn

from pls4all.sklearn import IntervalSelector
mdl = IntervalSelector(n_components=2, interval_width=10, step=5, n_folds=3)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

R · pls4all_method()

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("interval_select", X, y,
                      n_components = 4L, params = list(interval_width = 5L, interval_step = 2L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

MATLAB · pls4all (MEX)

res = pls4all.interval_select(X, y, 4);
% see header of bindings/matlab/+pls4all/interval_select.m for full
% parameter surface:
%   res = interval_select(X, Y, n_components, interval_width, step)
yhat = predict(res, Xtest);

MATLAB · pls4all (classdef)

No idiomatic classdef wrapper — invoke pls4all.fit("interval_select", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

• 📐 ref.r_mdatools (R · r) — mdatools 0.15.0 · strict (rmse_rel ≤ 1e-06) — R mdatools::ipls forward-iPLS — returns the union of selected interval variables. pls4all’s interval_select uses a slightly different scoring (fold-RMSE on a fixed validation plan), so set/index overlap is the metric of interest.

Benchmarks

Adaptive wall-clock per cell measured against full_matrix.csv. 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  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ 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). 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.

1 thread

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	1.5 s
Python · pls4all
pls4all.python	✓ J 1.00	1.5 s
pls4all.sklearn	⇄ J 0.50	3.75 ms🏆
R · pls4all
pls4all.R	⇄ J 0.50	10.9 ms
pls4all.R.formula	⇄ J 0.50	11.7 ms
pls4all.R.mdatools	⇄ J 0.50	13.9 ms
pls4all.R.pls	⇄ J 0.50	10.3 ms
R · external
📐ref.r_mdatools	source	632.3 ms

3 threads

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	2.0 s
Python · pls4all
pls4all.python	✓ J 1.00	2.0 s
pls4all.sklearn	⇄ J 0.50	3.95 ms🏆
R · pls4all
pls4all.R	⇄ J 0.50	8.51 ms
pls4all.R.formula	⇄ J 0.50	9.33 ms
pls4all.R.mdatools	⇄ J 0.50	7.09 ms
pls4all.R.pls	⇄ J 0.50	9.36 ms
R · external
📐ref.r_mdatools	source	706.6 ms

10 threads

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	1.1 s
Python · pls4all
pls4all.python	✓ J 1.00	994.2 ms
pls4all.sklearn	⇄ J 0.50	2.26 ms🏆
R · pls4all
pls4all.R	⇄ J 0.50	5.63 ms
pls4all.R.formula	⇄ J 0.50	6.68 ms
pls4all.R.mdatools	⇄ J 0.50	6.61 ms
pls4all.R.pls	⇄ J 0.50	7.03 ms
R · external
📐ref.r_mdatools	source	507.0 ms

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See also: benchmark overview · methods index · interactive dashboard