Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
This provides a robust statistical testing method for applications requiring data-driven, distribution-free approaches, though it appears incremental in advancing existing robust testing frameworks.
The authors tackled the problem of robust hypothesis testing by developing a computationally efficient framework using Wasserstein uncertainty sets, achieving a nearly-optimal detector with complexity independent of observation space dimension and demonstrated excellent performance on human activity data.
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.