IFML Seminar: 03/28/25 - Simple Binary Hypothesis Testing: One-shot Bayes Error Bounds and Reverse Data-processing Inequalities

Abstract: In this talk, we first discuss a new one-shot lower bound on the Bayes error in simple binary hypothesis testing. This bound leads to a new proof of the formula for the sample complexity of simple binary hypothesis testing, first derived in Pensia et al. (2024). It also enables us to show that sequential interaction does not help reduce the sample complexity of distributed hypothesis testing, resolving an open problem from prior work. We also discuss a new reverse data-processing inequality that tightens the sample complexity bounds for distributed hypothesis testing under communication constraints, solving another open problem from prior work.

Bio: Varun Jog is Professor of Information Theory and Statistics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge. His research interests lie in the areas of information theory, machine learning, and statistics.