# Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders

@inproceedings{Yan2021KernelTT, title={Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders}, author={Jie Yan and Xianyang Zhang}, year={2021} }

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the maximum mean discrepancy (MMD) with the kernel of the form k(x, y) = f(‖x− y‖2/γ), including MMD with the Gaussian kernel and the Laplacian kernel, and the energy distance as special cases. We derive asymptotic expansions of the kernel two-sample statistics…

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