Year: 2024
Type: preprint
Abstract: We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator. Our bounds are non-asymptotic and are expressed in terms of the number of observations, the noise level, the properties of the design matrix, and the number of considered PLS components. In particular, we exhibit some scenarios where the variability of the PLS may explode and prove that we can get round of these situations by introducing a Ridge regularization step. These theoretical findings are illustrated by some numerical simulations.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403407100