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Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
RUI GAO · Liyan Xie · Yao Xie · Huan Xu

Thu Dec 06 01:50 PM -- 01:55 PM (PST) @ Room 517 CD

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.

Author Information

RUI GAO (GEORGIA TECH)
Liyan Xie (Georgia Institute of Technology)
Yao Xie (Georgia Institute of Technology)

Yao Xie is an Assistant Professor and Harold R. and Mary Anne Nash Early Career Professor in the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, which she joined in 2013. She received her Ph.D. in Electrical Engineering (minor in Mathematics) from Stanford University in 2011, M.Sc. in Electrical and Computer Engineering from the University of Florida, and B.Sc. in Electrical Engineering and Computer Science from University of Science and Technology of China (USTC) . From 2012 to 2013, she was a Research Scientist at Duke University. Her research areas include statistics, signal processing, and machine learning, in providing theoretical foundation as well as developing computationally efficient and statistically powerful algorithms for big data in various applications such as sensor networks, imaging, and crime data analysis. She received the National Science Foundation CAREER Award in 2017 and her crime data analytics project received the Smart 50 Award at the Smart Cities Connect Conferences and Expo in 2018.

Huan Xu (Georgia Inst. of Technology)

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