Robust Kernel Hypothesis Testing under Data Corruption

2024-05-30

arXiv.org

AI Summary

This paper addresses hypothesis testing under contaminated data—including adversarial perturbations—by proposing the first non-asymptotic robust kernel permutation test framework. The method leverages kernel embeddings, the maximum mean discrepancy (MMD), and the Hilbert–Schmidt independence criterion (HSIC), and robustifies the permutation procedure to strictly control Type-I error in finite samples while ensuring consistent statistical power. Theoretically, the framework achieves the first non-asymptotic minimax optimality for both two-sample and independence testing under contamination, with provably superior robustness compared to existing differentially private hypothesis tests. Extensive experiments demonstrate its high power under realistic data contamination scenarios. An open-source implementation is provided for plug-and-play deployment.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Natural Language Processing: Safety and Robustness

Application Category

• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Robust hypothesis testing under data corruption
• Control non-asymptotic type I error
• Minimax optimal kernel robust tests

Innovation

• Robust permutation tests method
• Minimax optimal kernel tests
• Adaptable private tests robustness