The Price of Tolerance in Distribution Testing

Abstract

We revisit the problem of tolerant distribution testing. That is, given samples from an unknown distribution p over {1, . . . , n}, is it ε1-close to or ε2-far from a reference distribution q (in total variation distance)? Despite significant interest over the past decade, this problem is well understood only in the extreme cases. In the noiseless setting (i.e., ε1 = 0) the sample complexity is Θ( √ n), strongly sublinear