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Generalization bounds for nonparametric regression with β−mixing samples

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03311506
Contributor : David Barrera Connect in order to contact the contributor
Submitted on : Sunday, August 1, 2021 - 2:24:49 AM
Last modification on : Wednesday, August 4, 2021 - 3:35:21 AM

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

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