Robust Hypothesis Testing Using Wasserstein Uncertainty Sets

Rui Gao; Liyan Xie; Yao Xie; Huan Xu

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arXiv · 1805.10611

Robust Hypothesis Testing Using Wasserstein Uncertainty Sets

Rui Gao·Liyan Xie·Yao Xie·Huan Xu

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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.

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BibTeX RIS

Rui Gao, Liyan Xie, Yao Xie, Huan Xu. 2018-05-27. Robust Hypothesis Testing Using Wasserstein Uncertainty Sets. https://arxiv.org/abs/1805.10611

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