Kernel two-sample tests in high dimensions: interplay between moment discrepancy and dimension-and-sample orders
高维核两样本检验：矩差异与维数、样本量阶数的相互作用
Summary Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behaviour of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the maximum mean discrepancy using an isotropic kernel, which includes maximum mean discrepancy with the Gaussian kernel and the Laplace kernel, and the energy distance as special cases. We derive asymptotic expansions of the kernel…