Professor Po-Ling Loh, University of Cambridge
Hypothesis testing under information constraints
Abstract
This talk will cover a series of recent results concerning the sample complexity of hypothesis testing under various constraints. A fundamental result in classical statistics concerns the optimality of the likelihood ratio test for a simple hypothesis test between two distributions. However, what if the i.i.d. samples from the underlying distribution are not observed precisely, but must be passed through a noisy channel (e.g., quantizing continuous data, or introducing randomness to preserve privacy)? We show how to characterize the sample complexity of such problems, and present computationally feasible methods to implement optimal strategies. We also show how the same algorithms may be used to derive optimal robust hypothesis tests even when data are drawn from a Huber contamination ball around the fixed distributions. Time permitting, we will discuss results on the sample complexity of a Bayesian version of hypothesis testing, where the two hypotheses have unequal priors. This is joint work with Ankit Pensia and Varun Jog.