We develop a general framework for data-driven robust hypothesis testing with Wasserstein uncertainty sets constructed using small sets of “training samples”. Our goal is to find the optimal test that minimizes the worst-case risk over uncertainty sets. We develop an efficient approach to solve this minimax problem: using strong duality, we convert the problem into a tractable reformulation, where we first establish closed-form optimal tests for a given collection of distributions and then solve the least favorable distributions over the uncertainty sets using a convex optimization problem. We extend our framework to multiple observations using the majority vote principle and discuss the generalization property. Synthetic and real data show the good performance of our approach.

This is joint work with Dr. Rui Gao and Dr. Yao Xie.