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November 2019 Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
Gilles Blanchard, Oleksandr Zadorozhnyi
Bernoulli 25(4B): 3421-3458 (November 2019). DOI: 10.3150/18-BEJ1095

Abstract

We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a $\tau$-mixing process.

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Gilles Blanchard. Oleksandr Zadorozhnyi. "Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods." Bernoulli 25 (4B) 3421 - 3458, November 2019. https://doi.org/10.3150/18-BEJ1095

Information

Received: 1 January 2018; Revised: 1 October 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110143
MathSciNet: MR4010960
Digital Object Identifier: 10.3150/18-BEJ1095

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4B • November 2019
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