A Unified View of Optimal Kernel Hypothesis Testing

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.

@article{schrab2025_2503.07084,
  title={ A Unified View of Optimal Kernel Hypothesis Testing },
  author={ Antonin Schrab },
  journal={arXiv preprint arXiv:2503.07084},
  year={ 2025 }
}