# `iriv_select` — IRIV — Iteratively Retaining Informative Variables _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description Iteratively Retains Informative Variables (Phase 51) From the `pls4all.sklearn.IRIVSelector` docstring: > IRIV — Iteratively Retains Informative Variables (Yun 2014). > **Registry note** — NumPy port of libPLS `iriv` (Yun 2014). Mann-Whitney U test via `scipy.stats.mannwhitneyu`. Default `_iriv_select_pls4all` path invokes the same NumPy function with `np.random.default_rng(seed)`, giving bit-exact mask parity. The C++ splitmix64 kernel is opt-in via `legacy=True`. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `max_rounds` | `int` | `5` | Maximum rounds of strongly/weakly informative reclassification. | | `n_folds` | `int` | `5` | Number of cross-validation folds used inside the selector. | | `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. | | `fold` | `int` | `3` | registry benchmark cell value | ## Explanations ### Bibliographic source Yun, Y. H., Wang, W. T., Tan, M. L., Liang, Y. Z., Li, H. D., Cao, D. S., Lu, H. M. & Xu, Q. S. (2014). *A strategy that iteratively retains informative variables for selecting optimal variable subset in multivariate calibration*. Analytica Chimica Acta 807, 36–43. ### Mathematical principle IRIV classifies each variable into four categories at each iteration: **strongly informative**, **weakly informative**, **uninformative**, **interfering**. The first two are retained, the last two eliminated. Iteration continues until no further interfering variables remain. Categories are determined by Monte-Carlo subset analysis with a permutation-based reference distribution: each variable's CV-RMSE contribution distribution is compared against the distribution under random subset inclusion. This four-way classification is more nuanced than single-threshold methods and tends to handle correlated predictors well (correlated features can both be 'weakly informative'). ### Implementation `n4m_iriv_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_iriv_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 iriv_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = iriv_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 IRIVSelector mdl = IRIVSelector(n_components=2, max_rounds=5, n_folds=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("iriv_select", X, y, n_components = 4L, params = list(max_rounds = 3L, fold = 3L, 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.iriv_select(X, y, 4); % see header of bindings/matlab/+pls4all/iriv_select.m for full % parameter surface: % res = iriv_select(X, Y, n_components, max_rounds, seed) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("iriv_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_iriv_numpy_port`** (python · python) — `iriv_numpy_port` 1.0.0 · strict (rmse_rel ≤ 1e-06) — NumPy port of libPLS `iriv` (Yun 2014). Mann-Whitney U test via `scipy.stats.mannwhitneyu`; binary-matrix sampler keyed to `np.random.default_rng(seed)` for bit-exact reproducibility. ::: ### 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
BackendParity50×250 (ms)80×25 (ms)100×50 (ms)100×500 (ms)100×2500 (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≈21.3 s403.9 ms16.8 s——1.5 s25.5 s——125.3 s——540.6 s—
pls4all.cpp.blas+omp≈21.1 s401.5 ms17.8 s——1.5 s25.8 s——109.4 s🏆——471.5 s🏆—
pls4all.cpp.omp≈21.0 s🏆426.9 ms16.9 s——1.5 s30.9 s——127.9 s——527.6 s—
pls4all.cpp.ref≈21.2 s408.0 ms16.7 s🏆——1.5 s🏆24.1 s🏆——126.4 s——510.8 s—
Python · pls4all
pls4all.python✓ bind21.9 s418.1 ms———1.5 s————————
pls4all.sklearn✗ +1e+005.0 s26.5 ms———369.3 ms————————
R · pls4all
pls4all.R✗ +1e+006.3 s39.9 ms———488.3 ms————————
pls4all.R.formula✗ +1e+006.3 s38.7 ms———481.1 ms————————
pls4all.R.mdatools✗ +1e+006.3 s34.8 ms———481.2 ms————————
pls4all.R.pls✗ +1e+006.1 s34.8 ms———493.6 ms————————
MATLAB · pls4all
pls4all.matlab✗ +1e+004.6 s28.3 ms———464.5 ms————————
pls4all.matlab.classdef✗ +1e+004.6 s29.2 ms———466.3 ms————————
Python · external
📐ref.python_iriv_numpy_portsource21.7 s335.9 ms🏆———1.9 s————————
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity50×250 (ms)80×25 (ms)100×50 (ms)100×500 (ms)100×2500 (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—286.1 ms————————————
pls4all.cpp.blas+omp✓ ref—285.8 ms————————————
pls4all.cpp.omp✓ ref—285.7 ms————————————
pls4all.cpp.ref✓ ref—285.2 ms🏆————————————
Python · pls4all
pls4all.python✓ bind—304.6 ms————————————
pls4all.sklearn✗ +1e+00—25.3 ms————————————
R · pls4all
pls4all.R✗ +1e+00—30.0 ms————————————
pls4all.R.formula✗ +1e+00—30.8 ms————————————
pls4all.R.mdatools✗ +1e+00—31.7 ms————————————
pls4all.R.pls✗ +1e+00—30.9 ms————————————
MATLAB · pls4all
pls4all.matlab✗ +1e+00—26.4 ms————————————
pls4all.matlab.classdef✗ +1e+00—26.9 ms————————————
Python · external
📐ref.python_iriv_numpy_portsource—306.4 ms————————————
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity50×250 (ms)80×25 (ms)100×50 (ms)100×500 (ms)100×2500 (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—278.6 ms————————————
pls4all.cpp.blas+omp✓ ref—276.6 ms🏆————————————
pls4all.cpp.omp✓ ref—278.0 ms————————————
pls4all.cpp.ref✓ ref—277.1 ms————————————
Python · pls4all
pls4all.python✓ bind—315.8 ms————————————
pls4all.sklearn✗ +1e+00—24.3 ms————————————
R · pls4all
pls4all.R✗ +1e+00—28.7 ms————————————
pls4all.R.formula✗ +1e+00—29.5 ms————————————
pls4all.R.mdatools✗ +1e+00—30.0 ms————————————
pls4all.R.pls✗ +1e+00—29.5 ms————————————
MATLAB · pls4all
pls4all.matlab✗ +1e+00—24.1 ms————————————
pls4all.matlab.classdef✗ +1e+00—25.0 ms————————————
Python · external
📐ref.python_iriv_numpy_portsource—284.0 ms————————————
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)