| Paper ID | D7-S2-T3.3 |
| Paper Title |
A Data-Driven Approach to Robust Hypothesis Testing Using Kernel MMD Uncertainty Sets |
| Authors |
Zhongchang Sun, Shaofeng Zou, University at Buffalo, the State University of New York, United States |
| Session |
D7-S2-T3: Hypothesis Testing |
| Chaired Session: |
Tuesday, 20 July, 22:20 - 22:40 |
| Engagement Session: |
Tuesday, 20 July, 22:40 - 23:00 |
| Abstract |
THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. The problem of robust hypothesis testing is studied, where under the null and alternative hypotheses, data generating distributions are assumed to belong to some uncertainty sets. In this paper, centers of the uncertainty sets are constructed in a data-driven manner, i.e., they are empirical distributions of training samples from the null and alternative hypotheses, respectively. The Neyman-Pearson setting is investigated, where the goal is to minimize the worst-case probability of miss detection over all possible distributions in the uncertainty set of the alternative hypothesis subject to the constraint on the worst-case probability of false alarm over all possible distributions in the uncertainty set of the null hypothesis. A robust test based on MMD is proposed and is further shown to be asymptotically optimal. We further provide some numerical results to demonstrate the performance of the proposed robust test.
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