Article Dans Une Revue Scandinavian Journal of Statistics Année : 2025

A non-asymptotic analysis of the single component PLS regression

Résumé

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that 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 test on the first PLS component. In a second time, we extend these results to the sparse partial least squares (sPLS) 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.

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Dates et versions

hal-04237950 , version 1 (11-10-2023)

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Luca Castelli, Irène Gannaz, Clément Marteau. A non-asymptotic analysis of the single component PLS regression. Scandinavian Journal of Statistics, 2025, 52 (4), pp.2314-2351. ⟨10.1111/sjos.70028⟩. ⟨hal-04237950⟩
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