# Robust Kernel Hypothesis Testing under Data Corruption

arXiv: https://arxiv.org/abs/2405.19912 · HTML: https://mlsanity.com/paper/2405.19912/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 83 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 39)

- [Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixtures](https://mlsanity.com/paper/1611.03473/) (2016)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Differentially Private Assouad, Fano, and Le Cam](https://mlsanity.com/paper/2004.06830/) (2020)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy](https://mlsanity.com/paper/1909.13339/) (2019)
- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence](https://mlsanity.com/paper/1912.05737/) (2019)
- [On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives](https://mlsanity.com/paper/1909.03302/) (2019)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [A Permutation-free Kernel Two-Sample Test](https://mlsanity.com/paper/2211.14908/) (2022)
- [Spectral Regularized Kernel Two-Sample Tests](https://mlsanity.com/paper/2212.09201/) (2022)
- [FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test](https://mlsanity.com/paper/1405.2664/) (2014)
- [On robustness and local differential privacy](https://mlsanity.com/paper/2201.00751/) (2022)
- [Compress Then Test: Powerful Kernel Testing in Near-linear Time](https://mlsanity.com/paper/2301.05974/) (2023)
- [Test without Trust: Optimal Locally Private Distribution Testing](https://mlsanity.com/paper/1808.02174/) (2018)
- [Differentially Private Nonparametric Hypothesis Testing](https://mlsanity.com/paper/1903.09364/) (2019)
- [Priv'IT: Private and Sample Efficient Identity Testing](https://mlsanity.com/paper/1703.10127/) (2017)
- [Post Selection Inference with Incomplete Maximum Mean Discrepancy Estimator](https://mlsanity.com/paper/1802.06226/) (2018)
- [A Permutation-Free Kernel Independence Test](https://mlsanity.com/paper/2212.09108/) (2022)
- [A simpler condition for consistency of a kernel independence test](https://mlsanity.com/paper/1501.06103/) (2015)
- [Boosting the Power of Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.10687/) (2023)
- [Differentially Private Permutation Tests](https://mlsanity.com/paper/2310.19043/) (2023)
- [A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2202.04258/) (2022)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanism](https://mlsanity.com/paper/2208.06803/) (2022)
- [The Full Landscape of Robust Mean Testing: Sharp Separations between Oblivious and Adaptive Contamination](https://mlsanity.com/paper/2307.10273/) (2023)

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

- [A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSD](https://mlsanity.com/paper/2503.04820/) (2025)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing](https://mlsanity.com/paper/2510.11140/) (2025)
- [A Unified View of Optimal Kernel Hypothesis Testing](https://mlsanity.com/paper/2503.07084/) (2025)
- [Regularized f-Divergence Kernel Tests](https://mlsanity.com/paper/2601.19755/) (2026)
- [Kernel Tests of Equivalence](https://mlsanity.com/paper/2603.10886/) (2026)

## Abstract (arXiv)

We propose a general method for constructing robust permutation tests under data corruption. The proposed tests effectively control the non-asymptotic type I error under data corruption, and we prove their consistency in power under minimal conditions. This contributes to the practical deployment of hypothesis tests for real-world applications with potential adversarial attacks. For the two-sample and independence settings, we show that our kernel robust tests are minimax optimal, in the sense that they are guaranteed to be non-asymptotically powerful against alternatives uniformly separated from the null in the kernel MMD and HSIC metrics at some optimal rate (tight with matching lower bound). We point out that existing differentially private tests can be adapted to be robust to data corruption, and we demonstrate in experiments that our proposed tests achieve much higher power than these private tests. Finally, we provide publicly available implementations and empirically illustrate the practicality of our robust tests.