A Kernel Two-Sample Test

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Journal of Machine Learning Research 13 (2012) 723-773Submitted 4/08; Revised 11/11; Published 3/12A Kernel Two-Sample TestArthur Gretton for Intelligent SystemsSpemannstrasse 3872076 T ubingen, GermanyKarsten M. Borgwardt Learning and Computational Biology Research GroupMax Planck Institutes T ubingenSpemannstrasse 3872076 T ubingen, GermanyMalte J. Rasch XinJieKouWai Key Laboratory of Cognitive Neuroscience and Learning,Beijing Normal University,Beijing, 100875, ChinaBernhard Sch for Intelligent SystemsSpemannstrasse 3872076, T ubingen, GermanyAlexander Smola Research2821 Mission College BlvdSanta Clara, CA 95054, USAEditor:Nicolas VayatisAbstractWe propose a framework for analyzing and comparing distributions, which we use to construct sta-tistical tests to determine if two samples are drawn from different distributions. Our test statistic isthe largest difference in expectations over functions in the unit ball of a reproducing Kernel Hilbertspace (RKHS), and is called themaximum mean discrepancy(MMD).

Kolmogorov-Smirnov and Earth-Mover’s distances, which are based ondifferent function classes; collectively these are known as integral probability metrics (Muller, 1997). On a more practical¨ note, the MMD has a reasonable computational cost, when compared with …

  Tests, Samples, Kolmogorov, Two sample test