# Robust Hypothesis Testing Using Wasserstein Uncertainty Sets

arXiv: https://arxiv.org/abs/1805.10611 · HTML: https://mlsanity.com/paper/1805.10611/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2018.

## Built on by (most cited first, 28 of 28)

- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [A Finite Sample Complexity Bound for Distributionally Robust Q-learning](https://mlsanity.com/paper/2302.13203/) (2023)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data](https://mlsanity.com/paper/2106.07636/) (2021)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts](https://mlsanity.com/paper/2106.00322/) (2021)
- [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)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (2024)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Conformal Prediction Regions are Imprecise Highest Density Regions](https://mlsanity.com/paper/2502.06331/) (2025)
- [Kernel Robust Hypothesis Testing](https://mlsanity.com/paper/2203.12777/) (2022)
- [Uncertainty-Aware Robust Learning on Noisy Graphs](https://mlsanity.com/paper/2306.08210/) (2023)
- [A Unified Data Representation Learning for Non-parametric Two-sample Testing](https://mlsanity.com/paper/2412.00613/) (2024)
- [Class-conditioned Domain Generalization via Wasserstein Distributional Robust Optimization](https://mlsanity.com/paper/2109.03676/) (2021)
- [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)
- [Robust Graph Learning Under Wasserstein Uncertainty](https://mlsanity.com/paper/2105.04210/) (2021)
- [Adversarial Attack and Defense for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2202.03077/) (2022)
- [Generalizing to Unseen Domains with Wasserstein Distributional Robustness under Limited Source Knowledge](https://mlsanity.com/paper/2207.04913/) (2022)
- [On the Adversarial Robustness of Benjamini Hochberg](https://mlsanity.com/paper/2501.03402/) (2025)
- [Optimal Transport for ε-Contaminated Credal Sets: To the Memory of Sayan Mukherjee](https://mlsanity.com/paper/2410.03267/) (2024)
- [Hypothesis Testing in Imaging Inverse Problems](https://mlsanity.com/paper/2505.22481/) (2025)
- [Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing](https://mlsanity.com/paper/2608.22746/) (2026)

## Abstract (arXiv)

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.