A new Universal Resample Stable Bootstrap-based Stopping Criterion in PLS Components Construction

TL;DR

This paper introduces a universal, bootstrap-based stopping criterion for PLS components that enhances stability and predictive accuracy across different regression frameworks and noise conditions.

Contribution

A novel, robust stopping criterion for PLSR and PLSGLR based on bootstrap resampling, improving stability and performance over classical methods.

Findings

Outperforms classical criteria in simulations

Demonstrates robustness across noise levels

Achieves better predictive accuracy in real data

Abstract

We develop a new robust stopping criterion in Partial Least Squares Regressions (PLSR) components construction characterised by a high level of stability. This new criterion is defined as a universal one since it is suitable both for PLSR and its extension to Generalized Linear Regressions (PLSGLR). This criterion is based on a non-parametric bootstrap process and has to be computed algorithmically. It allows to test each successive components on a preset significant level alpha. In order to assess its performances and robustness with respect to different noise levels, we perform intensive datasets simulations, with a preset and known number of components to extract, both in the case n>p (n being the number of subjects and p the number of original predictors), and for datasets with n<p. We then use t-tests to compare the performance of our approach to some others classical criteria. The property of robustness is particularly tested through resampling processes on a real allelotyping dataset. Our conclusion is that our criterion presents also better global predictive performances, both in the PLSR and PLSGLR (Logistic and Poisson) frameworks.