Replicable Distribution Testing

Ilias Diakonikolas (University of Wisconsin-Madison) · Jingyi Gao (University Of Wisconsin Madison) · Daniel Kane (UCSD) · Sihan Liu (Computer Science and Engineering Department, University of California, San Diego) · Christopher Ye (University of California San Diego)
algorithmic replicabilitydiscrete distributionsdistribution testingindependence testinglower boundsmethodologynatural propertiesnear-optimal boundsopen questionprobability distributionsreplicable algorithmsreplicable uniformity testingsample complexitysample complexity lower boundstesting closeness

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