A Unified View of Optimal Kernel Hypothesis Testing
This work provides a unified theoretical foundation for kernel-based hypothesis testing, which is incremental but addresses multiple constraints relevant for practitioners in machine learning and statistics.
The paper tackles the problem of optimal kernel hypothesis testing across MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks, presenting minimax optimal separation rates and adaptive kernel selection methods under constraints like computational efficiency and differential privacy.
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.