Robust Hypothesis Testing with Wasserstein Uncertainty Sets

TL;DR

This paper introduces a robust hypothesis testing framework using Wasserstein distance to improve performance under limited data scenarios, with applications in healthcare and anomaly detection.

Contribution

It develops a new non-parametric testing method based on distributionally robust optimization with Wasserstein uncertainty sets, including a tractable convex reformulation.

Findings

The proposed test is more robust with limited samples.

Convex reformulation enables efficient computation.

Method performs well on synthetic and real datasets.

Abstract

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a new non-parametric hypothesis testing framework based on distributionally robust optimization, which is more robust when there are limited samples for one or both hypotheses. Such a scenario often arises from applications such as health care, online change-point detection, and anomaly detection. We study the computational and statistical properties of the proposed test by presenting a tractable convex reformulation of the original infinite-dimensional variational problem exploiting Wasserstein's properties and characterizing the radii selection for the uncertainty sets. We also demonstrate the good performance of our method on synthetic and real data.