Interactive Hypothesis Testing Against Independence

Abstract—A hypothesis testing problem with communication constraints is studied, in which two nodes interactively commu-nicate with each other in q rounds to perform a simple binary hypothesis testing on whether the observed random sequences at the nodes are generated independently or not. The optimal tradeoff between the communication rates in q rounds interaction and the testing performance measured by the type II error exponent such that the type I error probability asymptotically vanishes. An example is provided that shows that a two-way test outperforms the optimal one-way test and thus that interaction helps for hypothesis testing. I