A Unified View of Optimal Kernel Hypothesis Testing

• URL: http://arxiv.org/abs/2503.07084v1
• Date: Mon, 10 Mar 2025 09:06:40 GMT
• Title: A Unified View of Optimal Kernel Hypothesis Testing
• Authors: Antonin Schrab,
• Abstract summary: This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks.<n>Minimax optimal separation rates in the kernel and $L2$ metrics are presented, with two adaptive kernel selection methods.
• Score: 3.1727619150610837
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with two adaptive kernel selection methods (kernel pooling and aggregation), and under various testing constraints: computational efficiency, differential privacy, and robustness to data corruption. Intuition behind the derivation of the power results is provided in a unified way accross the three frameworks, and open problems are highlighted.

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