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May 2019 A Bernstein-type inequality for functions of bounded interaction
Andreas Maurer
Bernoulli 25(2): 1451-1471 (May 2019). DOI: 10.3150/18-BEJ1026

Abstract

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein’s inequality from sums to more general functions, whose variation in any argument does not depend too much on the other arguments. Applications sharpen existing bounds for U-statistics and the generalization error of regularized least squares.

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Andreas Maurer. "A Bernstein-type inequality for functions of bounded interaction." Bernoulli 25 (2) 1451 - 1471, May 2019. https://doi.org/10.3150/18-BEJ1026

Information

Received: 1 February 2017; Revised: 1 January 2018; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049412
MathSciNet: MR3920378
Digital Object Identifier: 10.3150/18-BEJ1026

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

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Vol.25 • No. 2 • May 2019
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