Replicable Distribution Testing

TL;DR

This paper systematically studies distribution testing under the framework of algorithmic replicability, introducing new algorithms and lower bounds for testing properties like closeness, independence, and uniformity of distributions.

Contribution

It develops new replicable algorithms for distribution property testing and introduces a novel methodology for proving lower bounds on sample complexity.

Findings

New replicable algorithms for testing distribution closeness and independence

A methodology for lower bounds in replicable distribution testing

Near-optimal sample complexity bounds for uniformity and closeness testing

Abstract

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample complexity of replicably testing natural properties of the underlying distributions. On the algorithmic front, we develop new replicable algorithms for testing closeness and independence of discrete distributions. On the lower bound front, we develop a new methodology for proving sample complexity lower bounds for replicable testing that may be of broader interest. As an application of our technique, we establish near-optimal sample complexity lower bounds for replicable uniformity testing -- answering an open question from prior work -- and closeness testing.