WNCG Seminar Series: Testing Properties of Distributions
Abstract: Given samples from an unknown distribution, p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C, by at least ε in total variation distance? This fundamental question has received substantial attention in Statistics and Computer Science. Nevertheless, even for basic classes of distributions such as monotone, log-concave, unimodal, or product, the optimal sample complexity is unknown. We provide optimal testers for these families.