1. Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
- Author
-
Gao, Rui, Xie, Liyan, Xie, Yao, and Xu, Huan
- Subjects
Statistics - Machine Learning ,Computer Science - Information Theory ,Computer Science - Learning ,Mathematics - Optimization and Control - Abstract
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered around the empirical distribution defined via Wasserstein metric, thus our approach is data-driven and free of distributional assumptions. We develop a convex safe approximation of the minimax formulation and show that such approximation renders a nearly-optimal detector among the family of all possible tests. By exploiting the structure of the least favorable distribution, we also develop a tractable reformulation of such approximation, with complexity independent of the dimension of observation space and can be nearly sample-size-independent in general. Real-data example using human activity data demonstrated the excellent performance of the new robust detector.
- Published
- 2018