Year: 2025
Type: article
Abstract: ABSTRACT This paper investigates some theoretical properties of the Partial Least Squares method. We focus our attention on the single‐component case, which provides a useful framework to understand the underlying mechanism. We provide a non‐asymptotic upper bound on the quadratic loss in prediction with high probability in a high‐dimensional regression context. The bound is attained thanks to a preliminary regularization on the first PLS component. In a second time, we extend these results to the sparse Partial Least Squares approach. In particular, we exhibit upper bounds similar to those obtained with the lasso algorithm, up to an additional restricted eigenvalue constraint on the design matrix.
DOI: 10.1111/sjos.70028
Authors: Luca Castelli, Irène Gannaz, Clément Marteau
Institutions: Lyon 1 Université, Centre National de la Recherche Scientifique, Institut Camille Jordan, Université Jean Monnet, Institut National des Sciences Appliquées de Lyon, Université Jean Monnet, Institut polytechnique de Grenoble, Laboratoire des Sciences pour la Conception, l'Optimisation et la Production, Université Grenoble Alpes
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415506823