Robust Kernel Hypothesis Testing under Data Corruption

TL;DR

This paper introduces a robust permutation testing framework that maintains control over error rates under data corruption, with optimal power guarantees and practical implementations for real-world applications.

Contribution

It develops a general method for robust kernel hypothesis tests that are minimax optimal and adaptable to data corruption, improving upon existing private tests.

Findings

Controls non-asymptotic type I error under data corruption

Achieves minimax optimal power against alternatives

Outperforms differentially private tests in experiments

Abstract

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.