# Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets

arXiv: https://arxiv.org/abs/2403.14822 · HTML: https://mlsanity.com/paper/2403.14822/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 19 of 19)

- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning](https://mlsanity.com/paper/2002.10790/) (2020)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Neural Tangent Kernel Maximum Mean Discrepancy](https://mlsanity.com/paper/2106.03227/) (2021)
- [Contextual Stochastic Bilevel Optimization](https://mlsanity.com/paper/2310.18535/) (2023)
- [A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2202.04258/) (2022)
- [Regularization for Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2205.08826/) (2022)
- [Robust Hypothesis Testing with Wasserstein Uncertainty Sets](https://mlsanity.com/paper/2105.14348/) (2021)
- [Statistical Limit Theorems in Distributionally Robust Optimization](https://mlsanity.com/paper/2303.14867/) (2023)
- [Kernel Robust Hypothesis Testing](https://mlsanity.com/paper/2203.12777/) (2022)
- [Provably Convergent Policy Optimization via Metric-aware Trust Region Methods](https://mlsanity.com/paper/2306.14133/) (2023)
- [Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems](https://mlsanity.com/paper/1808.05290/) (2018)
- [Entropy-regularized Wasserstein distributionally robust shape and topology optimization](https://mlsanity.com/paper/2209.01500/) (2022)
- [Minimax Robust Quickest Change Detection using Wasserstein Ambiguity Sets](https://mlsanity.com/paper/2204.13034/) (2022)
- [ALSO-X#: Better Convex Approximations for Distributionally Robust Chance Constrained Programs](https://mlsanity.com/paper/2302.01737/) (2023)
- [Second-Order Conic and Polyhedral Approximations of the Exponential Cone: Application to Mixed-Integer Exponential Conic Programs](https://mlsanity.com/paper/2106.09123/) (2021)

## Built on by (most cited first, 4 of 4)

- [Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances](https://mlsanity.com/paper/2405.15441/) (2024)
- [Regularization for Adversarial Robust Learning](https://mlsanity.com/paper/2408.09672/) (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)

We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional uncertainty sets are constructed to center around the empirical distribution derived from samples based on Sinkhorn discrepancy. Given that the objective involves non-convex, non-smooth probabilistic functions that are often intractable to optimize, existing methods resort to approximations rather than exact solutions. To tackle the challenge, we introduce an exact mixed-integer exponential conic reformulation of the problem, which can be solved into a global optimum with a moderate amount of input data. Subsequently, we propose a convex approximation, demonstrating its superiority over current state-of-the-art methodologies in literature. Furthermore, we establish connections between robust hypothesis testing and regularized formulations of non-robust risk functions, offering insightful interpretations. Our numerical study highlights the satisfactory testing performance and computational efficiency of the proposed framework.