# Robust Hypothesis Testing with Wasserstein Uncertainty Sets

arXiv: https://arxiv.org/abs/2105.14348 · HTML: https://mlsanity.com/paper/2105.14348/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2021.

## Built on by (most cited first, 7 of 7)

- [Flow-based Distributionally Robust Optimization](https://mlsanity.com/paper/2310.19253/) (2023)
- [A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2202.04258/) (2022)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Kernel Robust Hypothesis Testing](https://mlsanity.com/paper/2203.12777/) (2022)
- [Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2403.14822/) (2024)
- [Adversarial Attack and Defense for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2202.03077/) (2022)
- [Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing](https://mlsanity.com/paper/2608.22746/) (2026)

## Abstract (arXiv)

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.