The exact equivalence of distance and kernel methods in hypothesis testing

Cencheng Shen () and Joshua T. Vogelstein ()
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Cencheng Shen: University of Delaware
Joshua T. Vogelstein: Johns Hopkins University

AStA Advances in Statistical Analysis, 2021, vol. 105, issue 3, No 1, 385-403

Abstract: Abstract Distance correlation and Hilbert-Schmidt independence criterion are widely used for independence testing, two-sample testing, and many inference tasks in statistics and machine learning. These two methods are tightly related, yet are treated as two different entities in the majority of existing literature. In this paper, we propose a simple and elegant bijection between metric and kernel. The bijective transformation better preserves the similarity structure, allows distance correlation and Hilbert-Schmidt independence criterion to be always the same for hypothesis testing, streamlines the code base for implementation, and enables a rich literature of distance-based and kernel-based methodologies to directly communicate with each other.

Keywords: Distance covariance; Hilbert-Schmidt independence criterion; Strong negative-type metric; Characteristic kernel (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10182-020-00378-1

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