Equivalence of distance-based and RKHS-based statistics in hypothesis testing
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TLDR
In this paper, a unifying framework linking two classes of statistics used in two-sample and independence testing is presented, namely, the energy distance and distance covariances from the statistics literature; and the maximum mean discrepancy (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces.Abstract:
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a positive definite kernel, termed distance kernel, may be defined such that the MMD corresponds exactly to the energy distance. Conversely, for any positive definite kernel, we can interpret the MMD as energy distance with respect to some negative-type semimetric. This equivalence readily extends to distance covariance using kernels on the product space. We determine the class of probability distributions for which the test statistics are consistent against all alternatives. Finally, we investigate the performance of the family of distance kernels in two-sample and independence tests: we show in particular that the energy distance most commonly employed in statistics is just one member of a parametric family of kernels, and that other choices from this family can yield more powerful tests.read more
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References
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Book
Support Vector Machines
TL;DR: This book explains the principles that make support vector machines (SVMs) a successful modelling and prediction tool for a variety of applications and provides a unique in-depth treatment of both fundamental and recent material on SVMs that so far has been scattered in the literature.
Journal ArticleDOI
A kernel two-sample test
TL;DR: This work proposes a framework for analyzing and comparing distributions, which is used to construct statistical tests to determine if two samples are drawn from different distributions, and presents two distribution free tests based on large deviation bounds for the maximum mean discrepancy (MMD).
Book ChapterDOI
Kernel Principal Component Analysis
TL;DR: A new method for performing a nonlinear form of Principal Component Analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
Journal ArticleDOI
Measuring and testing dependence by correlation of distances
TL;DR: Distance correlation is a new measure of dependence between random vectors that is based on certain Euclidean distances between sample elements rather than sample moments, yet has a compact representation analogous to the classical covariance and correlation.