Applied Math And Analysis Seminar
Tuesday, September 20, 2022, 3:15pm, Physics 119
Liyan Xie (Chinese University of Hong Kong, Shenzhen)
Data-driven Robust Hypothesis Testing via Wasserstein Uncertainty Sets

Abstract:

We consider a data-driven robust hypothesis testing problem where the true data-generating distributions are unknown and indirectly observable through limited training samples. We first construct the distributional uncertainty sets that contain distributions within a certain Wasserstein distance from a nominal distribution estimated from the training samples. The learning task is to solve the optimal test that minimizes the worst-case error within the uncertainty sets. By exploiting the geometry of the Wasserstein distance, we show that this problem can be solved efficiently through a tractable linear program reformulation. We also construct a confidence region for the optimal oracle test and present the generalization bound. The proposed robust test has great potential in many other problems and applications such as health care, anomaly detection, classification, etc.

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