This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these discrepancies are presented, including the commonly-used V-statistics and U-statistics, as well as several forms of the more computationally-efficient incomplete U-statistics. The importance of the choice of kernel bandwidth is stressed, showing how it affects the behaviour of the discrepancy estimation. Adaptive estimators are introduced, which combine multiple estimators with various kernels, addressing the problem of kernel selection.

翻译：本文针对最大均值差异（MMD）、希尔伯特-施密特独立性准则（HSIC）及核斯坦因差异（KSD）三种核差异方法提供实用化介绍。文中系统阐述这些差异的多种估计量，包括常用的V统计量与U统计量，以及若干计算效率更高的不完全U统计量变体。研究重点强调了核带宽选择的重要性，阐明其对差异估计行为的影响机制。同时引入自适应估计量，通过融合多核函数下的估计结果以解决核选择难题。