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

arXiv: https://arxiv.org/abs/2202.04258 · HTML: https://mlsanity.com/paper/2202.04258/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 9 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Classification Logit Two-sample Testing by Neural Networks](https://mlsanity.com/paper/1909.11298/) (2019)
- [Anomaly detection in online social networks](https://mlsanity.com/paper/1608.00301/) (2016)
- [Robust Hypothesis Testing with Wasserstein Uncertainty Sets](https://mlsanity.com/paper/2105.14348/) (2021)
- [Class-conditioned Domain Generalization via Wasserstein Distributional Robust Optimization](https://mlsanity.com/paper/2109.03676/) (2021)

## Built on by (most cited first, 9 of 9)

- [Flow-based Distributionally Robust Optimization](https://mlsanity.com/paper/2310.19253/) (2023)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (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)
- [Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances](https://mlsanity.com/paper/2405.15441/) (2024)
- [Gaussian Derivative Change-point Detection for Early Warnings of Industrial System Failures](https://mlsanity.com/paper/2410.22594/) (2024)
- [Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2512.12550/) (2025)
- [Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing](https://mlsanity.com/paper/2608.22746/) (2026)

## Abstract (arXiv)

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.