A Unified View of Optimal Kernel Hypothesis Testing

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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Reproductions