Two-sample statistics based on anisotropic kernels

Published online

Journal Article

Abstract The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorporating local covariance matrices and constructing an anisotropic kernel. The kernel matrix is asymmetric; it computes the affinity between $n$ data points and a set of $n_R$ reference points, where $n_R$ can be drastically smaller than $n$. While the proposed statistic can be viewed as a special class of Reproducing Kernel Hilbert Space MMD, the consistency of the test is proved, under mild assumptions of the kernel, as long as $\|p-q\| \sqrt{n} \to \infty $, and a finite-sample lower bound of the testing power is obtained. Applications to flow cytometry and diffusion MRI datasets are demonstrated, which motivate the proposed approach to compare distributions.

Full Text

Duke Authors

Cited Authors

  • Cheng, X; Cloninger, A; Coifman, RR

Published Date

  • December 10, 2019

Published In

Published By

PubMed ID

  • 32929389

Pubmed Central ID

  • 32929389

Electronic International Standard Serial Number (EISSN)

  • 2049-8772

International Standard Serial Number (ISSN)

  • 2049-8764

Digital Object Identifier (DOI)

  • 10.1093/imaiai/iaz018

Language

  • en