Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
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.
Cite
@article{arxiv.1805.10611,
title = {Robust Hypothesis Testing Using Wasserstein Uncertainty Sets},
author = {Rui Gao and Liyan Xie and Yao Xie and Huan Xu},
journal= {arXiv preprint arXiv:1805.10611},
year = {2018}
}