Concentration of Lipschitz Functions of Negatively Dependent Variables

TL;DR

This paper investigates whether Lipschitz functions of negatively dependent variables exhibit concentration bounds akin to McDiarmid's inequality, proving such bounds under negative regression conditions and correcting previous proofs.

Contribution

It establishes concentration bounds for Lipschitz functions of negatively dependent variables under negative regression, improving upon prior incomplete proofs.

Findings

Proves concentration bounds for negatively dependent variables

Corrects earlier proof by Dubhashi and Ranjan

Extends McDiarmid's inequality to negative regression setting

Abstract

We explore the question whether Lipschitz functions of random variables under various forms of negative correlation satisfy concentration bounds similar to McDiarmid's inequality for independent random variables. We prove such a concentration bound for random variables satisfying the condition of negative regression, correcting an earlier proof by Dubhashi and Ranjan.