When Janson meets McDiarmid: Bounded difference inequalities under graph-dependence

TL;DR

This paper extends classical concentration inequalities to dependent random variables structured by forests, providing improved bounds for graph-dependent functions and broadening the applicability of McDiarmid's and Janson's inequalities.

Contribution

It introduces new concentration inequalities for dependent variables based on forest dependencies, enhancing existing bounds for graph-dependent functions.

Findings

Established concentration inequalities for Lipschitz functions with forest-based dependencies.

Improved Hoeffding-type bounds for decomposable functions of dependent variables.

Extended McDiarmid's inequality to dependent random variables.

Abstract

We establish concentration inequalities for Lipschitz functions of dependent random variables, whose dependencies are specified by forests. We also give concentration results for decomposable functions, improving Janson's Hoeffding-type inequality for the summation of graph-dependent bounded variables. These results extend McDiarmid's bounded difference inequality to the dependent cases.