Testing Identity of Structured Distributions

TL;DR

This paper introduces a unified, optimal-sample complexity method for identity testing of various structured distributions, significantly advancing the efficiency and simplicity of such statistical tests.

Contribution

It provides a unified approach that yields new, simple, and optimal-sample complexity testers for multiple classes of structured distributions.

Findings

Sample complexity is information-theoretically optimal.

Developed simple testers for t-flat, t-modal, log-concave, and MHR distributions.

Applicable to mixtures of structured distributions.

Abstract

We study the question of identity testing for structured distributions. More precisely, given samples from a {\em structured} distribution $q$ over $[n]$ and an explicit distribution $p$ over $[n]$, we wish to distinguish whether $q=p$ versus $q$ is at least $\epsilon$-far from $p$, in $L_1$ distance. In this work, we present a unified approach that yields new, simple testers, with sample complexity that is information-theoretically optimal, for broad classes of structured distributions, including $t$-flat distributions, $t$-modal distributions, log-concave distributions, monotone hazard rate (MHR) distributions, and mixtures thereof.