A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets

TL;DR

This paper introduces a data-driven robust hypothesis testing method using Sinkhorn distance to define uncertainty sets, resulting in more flexible detectors that outperform traditional Wasserstein-based tests in small-sample scenarios.

Contribution

It proposes a novel Sinkhorn distance-based approach for robust hypothesis testing, extending the support of least favorable distributions beyond training samples.

Findings

Outperforms Wasserstein robust tests in experiments

Provides more flexible detectors for small-sample scenarios

Validated on synthetic and real datasets

Abstract

Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional uncertainty sets centered around the empirical distribution from samples using Sinkhorn distance. Compared with the Wasserstein robust test, the corresponding least favorable distributions are supported beyond the training samples, which provides a more flexible detector. Various numerical experiments are conducted on both synthetic and real datasets to validate the competitive performances of our proposed method.