Testing Distribution Identity Efficiently

TL;DR

This paper improves the efficiency of distribution identity testing by reducing the running time of existing algorithms from linear to near square-root in the domain size, while maintaining sample complexity.

Contribution

The authors modify the existing distribution identity tester to achieve a near square-root running time without increasing the sample complexity.

Findings

Achieved a running time of O~(sqrt(n) * poly(1/epsilon))

Maintained the same sample complexity as previous methods

Enhanced the practical efficiency of distribution testing algorithms

Abstract

We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution on the same domain. While Batu, Fortnow, Fischer, Kumar, Rubinfeld, and White (FOCS 2001) proved that the sample complexity of the problem is O~(sqrt(n) * poly(1/epsilon)), the running time of their tester is much higher: O(n) + O~(sqrt(n) * poly(1/epsilon)). We modify their tester to achieve a running time of O~(sqrt(n) * poly(1/epsilon)).