Some Hoeffding- and Bernstein-type Concentration Inequalities

TL;DR

This paper develops new concentration inequalities for functions of independent variables under sub-gaussian and sub-exponential conditions, extending Rademacher complexity methods to broader classes.

Contribution

It introduces novel concentration inequalities applicable to Lipschitz functions and unbounded sub-exponential distributions, expanding theoretical tools in probability.

Findings

Proves concentration inequalities for sub-gaussian variables.

Extends Rademacher complexity methods to unbounded sub-exponential distributions.

Provides theoretical bounds useful for machine learning analysis.

Abstract

We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher complexities to Lipschitz function classes and unbounded sub-exponential distribution.