A New Approach for Testing Properties of Discrete Distributions

We study problems in distribution property testing: Given sample access to one or more unknown discrete distributions, we want to determine whether they have some global property or are -far from having the property in 1 distance. In this paper, we provide a simple and general approach to obtain upper bounds in this setting, by reducing 1-testing to 2-testing. Our reduction yields optimal 1-testers, by using a standard 2-tester as a black-box. Using our framework, we obtain sample–optimal and computationally efficient estimators for a wide variety of 1 distribution testing problems, including the following: identity testing to a fixed distribution, closeness testing between two unknown distributions (with equal/unequal sample sizes), independence testing (in any number of dimensions), closeness testing for collections of distributions, and testing khistograms. For most of these problems, we give the first optimal testers in the literature. Moreover, our estimators are significan...

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Ilias Diakonikolas, Daniel M. Kane
• Keywords: CORR 2016, Education