Testing conditional independence of discrete distributions
Clément L. Canonne, Ilias Diakonikolas, Daniel M. Kane, Alistair M. Stewart · 2018
We study the problem of testing *conditional independence* for discrete distributions. Specifically, given samples from a discrete random variable (X, Y, Z) on domain [ℓ1]×[ℓ2] × [n], we want to distinguish, with probability at least 2/3, between the case that X and Y are conditionally independent given Z from the case that (X, Y, Z) is є-far, in ℓ1-distance, from every distribution that has this property. Conditional independence is a concept of central importance in probability and statistics with important applications in various scientific domains. As such, the statistical task of testing conditional independence has been extensively studied in various forms within the statistics and econometrics community for nearly a century. Perhaps surprisingly, this problem has not been previously considered in the framework of distribution property testing and in particular no tester with *sublinear* sample complexity is known, even for the important special case that the domains of X and Y are binary.