Hoeffding-Style Concentration Bounds for Exchangeable Random Variables

TL;DR

This paper derives Hoeffding-style concentration inequalities for exchangeable random variables, revealing anti-symmetry in tail bounds and connecting finite sample means with distributional and population means.

Contribution

It introduces novel tail bounds for exchangeable variables that depend on the support of the de Finetti mixing measure, extending classical results beyond i.i.d. cases.

Findings

Provides upper tail bounds based on the largest mean in the mixing measure support.

Establishes lower tail bounds based on the smallest mean in the mixing measure support.

Bridges the gap between finite sample and distributional/ population means.

Abstract

We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a generalization of the i.i.d. setting. In contrast to the existing literature on this problem, our result provides an upper tail bound with respect to the largest mean of a distribution in the support of the de Finetti mixing measure, and not the population mean. Equivalently, we establish a lower tail bound with respect to the smallest mean of a distribution in the support of the de Finetti mixing measure. This bridges the gap between finite sample and population means of exchangeable random variables, and distributional means.