one_se_rule — One-SE rule for component selection

Group: Diagnostic · Registry tolerance: 1e-06

Description

One-SE component selection rule (§10)

Registry note — R pls::plsr(validation='CV', segment.type='consecutive', method='simpls', scale=FALSE) + onesigma rule. pls4all’s wrapper runs the same consecutive-fold CV with a SIMPLS kernel matching pls::simpls.fit bit-for-bit, then feeds the pooled per-component RMSEP into the C-side n4m_one_se_rule_compute. Per-component CV-RMSEP vectors agree to ~1e-12.

Parameters

Name

Type

Default

Notes

max_components

int

8

registry benchmark cell value

n_folds

int

5

registry benchmark cell value

Explanations

Bibliographic source

Hastie, T., Tibshirani, R. & Friedman, J. (2009). The Elements of Statistical Learning, 2nd ed., Springer, §7.10.

Mathematical principle

Cross-validated RMSE as a function of \(k\) is typically U-shaped with a relatively flat minimum. Picking the absolute minimum \(k^{\star}\) can over-fit because it exploits sampling noise. The one-SE rule instead picks the smallest \(k\) whose CV-RMSE is within one standard error of \(\mathrm{RMSE}(k^{\star})\).

This yields a more parsimonious model with negligible predictive cost — the smaller-\(k\) alternative is indistinguishable from the optimum within the noise of the CV estimate. The rule is non-parametric (no assumption about the CV-RMSE distribution) and is the standard practice in regularised regression (glmnet, pls::pls).

Inputs: a fold × component RMSE matrix from cross-validation. Output: an integer component count.

Implementation

n4m_one_se_rule_compute. Returns an integer.

MATLAB header (bindings/matlab/+pls4all/one_se_rule.m):

pls4all.one_se_rule  One-SE component selection from a fold RMSE matrix.
 fold_rmse_matrix: (max_components × n_folds) matrix of fold RMSE values.

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 */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_one_se_rule_compute(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);

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

from pls4all.sklearn import one_se_rule
result = one_se_rule(X, y, n_components=2)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("one_se_rule", X, y,
                      n_components = 2L, params = list(max_components = 8L, n_folds = 5L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.one_se_rule(X, y, 2);
% see header of bindings/matlab/+pls4all/one_se_rule.m for full
% parameter surface:
%   res = one_se_rule(fold_rmse_matrix)
yhat = predict(res, Xtest);

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

Registry parity references 📐

  • 📐 ref.r_pls (R · r) — pls 2.8.5 · strict (rmse_rel ≤ 1e-06) — R pls::plsr(validation='CV', segment.type='consecutive', method='simpls', scale=FALSE) + pls::selectNcomp(method='onesigma'). The pls4all wrapper performs the same consecutive-fold CV with a SIMPLS kernel matching pls::simpls.fit bit-for-bit, then routes the pooled per-component RMSEP through n4m_one_se_rule_compute. We compare mean_rmse_per_component directly.

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.

BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 4e-142.10 ms
Python · pls4all
pls4all.python✓ bind2.08 ms
pls4all.sklearn⇄ +9e-011.13 ms🏆
R · pls4all
pls4all.R⇄ +9e-013.25 ms
pls4all.R.formula⇄ +9e-013.87 ms
pls4all.R.mdatools⇄ +9e-013.96 ms
pls4all.R.pls⇄ +9e-014.01 ms
R · external
📐ref.r_plssource11.6 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 4e-147.61 ms
Python · pls4all
pls4all.python✓ bind2.19 ms
pls4all.sklearn⇄ +9e-011.23 ms🏆
R · pls4all
pls4all.R⇄ +9e-013.28 ms
pls4all.R.formula⇄ +9e-014.07 ms
pls4all.R.mdatools⇄ +9e-014.07 ms
pls4all.R.pls⇄ +9e-014.00 ms
R · external
📐ref.r_plssource11.6 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 4e-142.06 ms
Python · pls4all
pls4all.python✓ bind2.14 ms
pls4all.sklearn⇄ +9e-011.13 ms🏆
R · pls4all
pls4all.R⇄ +9e-012.80 ms
pls4all.R.formula⇄ +9e-015.64 ms
pls4all.R.mdatools⇄ +9e-014.37 ms
pls4all.R.pls⇄ +9e-014.60 ms
R · external
📐ref.r_plssource11.5 ms

See also: benchmark overview · methods index · interactive dashboard