# `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_feature_selection_bipls_select`. Reference: R `plsVarSel`. R roxygen note (`methods_extra.R::bipls_select`): > biPLS — backward interval PLS. > @param n_components Integer. Number of latent components. > @param interval_width Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param min_intervals Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export ### 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_feature_selection_bipls_select(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} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- bipls_select(X, Y, n_components, interval_width = 10L, min_intervals = 1L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{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  ·  ⇄ 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**: 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
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.003.83 ms
Python · pls4all
pls4all.python✓ J 1.003.60 ms🏆
pls4all.sklearn✓ J 1.003.69 ms
R · pls4all
pls4all.R✓ J 1.008.26 ms
pls4all.R.formula✓ J 1.0011.7 ms
pls4all.R.mdatools✓ J 1.009.90 ms
pls4all.R.pls✓ J 1.008.83 ms
R · external
📐ref.r_mdatoolssource365.6 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.003.49 ms🏆
Python · pls4all
pls4all.python✓ J 1.003.58 ms
pls4all.sklearn✓ J 1.003.74 ms
R · pls4all
pls4all.R✓ J 1.009.93 ms
pls4all.R.formula✓ J 1.0025.5 ms
pls4all.R.mdatools✓ J 1.0015.1 ms
pls4all.R.pls✓ J 1.0024.8 ms
R · external
📐ref.r_mdatoolssource1.0 s
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.0014.3 ms
Python · pls4all
pls4all.python✓ J 1.0013.4 ms
pls4all.sklearn✓ J 1.005.97 ms🏆
R · pls4all
pls4all.R✓ J 1.0023.9 ms
pls4all.R.formula✓ J 1.0035.4 ms
pls4all.R.mdatools✓ J 1.0016.3 ms
pls4all.R.pls✓ J 1.0021.7 ms
R · external
📐ref.r_mdatoolssource333.9 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)