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Two-sample statistics based on anisotropic kernels

Publication ,  Journal Article
Cheng, X; Cloninger, A; Coifman, RR
Published in: Information and Inference: A Journal of the IMA
December 10, 2019

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.

Duke Scholars

Published In

Information and Inference: A Journal of the IMA

DOI

EISSN

2049-8772

ISSN

2049-8764

Publication Date

December 10, 2019

Publisher

Oxford University Press (OUP)
 

Citation

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Chicago
ICMJE
MLA
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Cheng, X., Cloninger, A., & Coifman, R. R. (2019). Two-sample statistics based on anisotropic kernels. Information and Inference: A Journal of the IMA. https://doi.org/10.1093/imaiai/iaz018
Cheng, Xiuyuan, Alexander Cloninger, and Ronald R. Coifman. “Two-sample statistics based on anisotropic kernels.” Information and Inference: A Journal of the IMA, December 10, 2019. https://doi.org/10.1093/imaiai/iaz018.
Cheng X, Cloninger A, Coifman RR. Two-sample statistics based on anisotropic kernels. Information and Inference: A Journal of the IMA. 2019 Dec 10;
Cheng, Xiuyuan, et al. “Two-sample statistics based on anisotropic kernels.” Information and Inference: A Journal of the IMA, Oxford University Press (OUP), Dec. 2019. Manual, doi:10.1093/imaiai/iaz018.
Cheng X, Cloninger A, Coifman RR. Two-sample statistics based on anisotropic kernels. Information and Inference: A Journal of the IMA. Oxford University Press (OUP); 2019 Dec 10;
Journal cover image

Published In

Information and Inference: A Journal of the IMA

DOI

EISSN

2049-8772

ISSN

2049-8764

Publication Date

December 10, 2019

Publisher

Oxford University Press (OUP)