Testing Properties of Multiple Distributions with Few Samples

Abstract

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1,p_2,\dots ,p_s$, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the $p_i$'s are uniform or $\epsilon$-far from being uniform in ${\ell }_1$-distance (2) Identity Testing: Testing whether all the $p_i$'s are equal to an explicitly given distribution $q$ or $\epsilon$-far from $q$ in ${\ell }_1$-distance, and (3) Closeness Testing: Testing whether all the $p_i$'s are equal to a distribution $q$ which we have sample access to, or $\epsilon$-far from $q$ in ${\ell }_1$-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.

ITCS 2020

References in corpus (1)

• Maximum Likelihood Estimation for Learning Populations of Parameters