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  A Fast, Consistent Kernel Two-Sample Test

Gretton, A., Fukumizu, K., Harchaoui, Z., & Sriperumbudur, B. (2010). A Fast, Consistent Kernel Two-Sample Test. In Y. Bengio, D. Schuurmans, J. Lafferty, C. Williams, & A. Culotta (Eds.), Advances in Neural Information Processing Systems 22 (pp. 673-681). Red Hook, NY, USA: Curran.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-C0BC-3 Version Permalink: https://hdl.handle.net/21.11116/0000-0002-93CA-4
Genre: Conference Paper

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https://papers.nips.cc/paper/3738-a-fast-consistent-kernel-two-sample-test.pdf (Publisher version)
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 Creators:
Gretton, A1, 2, Author           
Fukumizu, K, Author           
Harchaoui, Z, Author           
Sriperumbudur, BK, Author           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: A kernel embedding of probability distributions into reproducing kernel Hilbert spaces (RKHS) has recently been proposed, which allows the comparison of two probability measures P and Q based on the distance between their respective embeddings: for a sufficiently rich RKHS, this distance is zero if and only if P and Q coincide. In using this distance as a statistic for a test of whether two samples are from different distributions, a major difficulty arises in computing the significance threshold, since the empirical statistic has as its null distribution (where P = Q) an infinite weighted sum of x2 random variables. Prior finite sample approximations to the null distribution include using bootstrap resampling, which
yields a consistent estimate but is computationally costly; and fitting a parametric model with the low order moments of the test statistic, which can work well in practice but has no consistency or accuracy guarantees. The main result of the present work is a novel estimate of the null distribution, computed from the eigenspectrum of the Gram matrix on the aggregate sample from P and Q, and having
lower computational cost than the bootstrap. A proof of consistency of this estimate is provided. The performance of the null distribution estimate is compared with the bootstrap and parametric approaches on an artificial example, high dimensional multivariate data, and text.

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 Dates: 2010-04
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 6132
 Degree: -

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Title: 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009)
Place of Event: Vancouver, BC, Canada
Start-/End Date: 2009-12-07 - 2009-12-10

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Title: Advances in Neural Information Processing Systems 22
Source Genre: Proceedings
 Creator(s):
Bengio, Y, Editor
Schuurmans, D, Editor
Lafferty, J, Editor
Williams, C, Editor
Culotta, A, Editor
Affiliations:
-
Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 673 - 681 Identifier: ISBN: 978-1-615-67911-9