Generalization bounds for nonparametric regression with β−mixing samples

David Barrera (1, 2) , Emmanuel Gobet (2)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of beta-mixing coefficients associated to the training sample. We then apply these results to some previously obtained inequalities for independent samples associated to the deviation of the least-squared error in nonparametric regression to derive corresponding generalization bounds for regression schemes in which the training sample may not be independent. These results provide a framework to analyze the error associated to regression schemes whose training sample comes from a large class of β−mixing sequences, including geometrically ergodic Markov samples, using only the independent case. More generally, they permit a meaningful extension of the Vapnik-Chervonenkis and similar theories for independent training samples to this class of β−mixing samples.

Domaines: Mathématiques [math]

David Barrera, Emmanuel Gobet. Generalization bounds for nonparametric regression with β−mixing samples. 2021. ⟨hal-03311506⟩