统一三类核检验方法，给出最优检测边界与自适应选核策略。
A Unified View of Optimal Kernel Hypothesis Testing
- 统一MMD、HSIC、KSD三类核检验框架的理论分析
- 提出两种自适应选核方法，实现计算效率与隐私保护平衡
- 适用于需要鲁棒性或差分隐私的统计检验场景
本文从统一视角探讨了MMD两样本检验、HSIC独立性检验和KSD拟合优度检验中的最优核检验问题。给出了在核范数和$L^2$范数下的最小最大最优分离率，提出两种自适应核选择方法（核池化与聚合），并在计算效率、差分隐私和抗数据污染等约束条件下进行分析。以统一方式解释了各类检验功效推导的直观原理，并指出了若干开放问题。
原文摘要 · Abstract (English)
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 across the three frameworks, and open problems are highlighted.
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