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.

References in corpus (7)

• BACH: Grand Challenge on Breast Cancer Histology Images
• Certifying Some Distributional Robustness with Principled Adversarial Training
• Robust Wasserstein Profile Inference and Applications to Machine Learning
• Distributionally Robust Logistic Regression
• Regularization via Mass Transportation
• Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
• Learning Probability Measures with respect to Optimal Transport Metrics

Cited by in corpus (13)

• Distributionally Robust Optimization: A Review
• Robust Hypothesis Testing Using Wasserstein Uncertainty Sets
• Sample Out-Of-Sample Inference Based on Wasserstein Distance
• Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes
• Minimax Robust Detection: Classic Results and Recent Advances
• Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning
• Confidence Regions in Wasserstein Distributionally Robust Estimation
• Interior-Point Methods Strike Back: Solving the Wasserstein Barycenter Problem
• Minimax Optimal Sequential Hypothesis Tests for Markov Processes
• Distributionally Robust Weighted $k$-Nearest Neighbors
• Kernel Hypothesis Testing with Set-valued Data
• Robust Mean Estimation on Highly Incomplete Data with Arbitrary Outliers
• Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data