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Conference Paper

A Kernel Method for the Two-Sample-Problem

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Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., & Smola, A. (2007). A Kernel Method for the Two-Sample-Problem. In B. Schölkopf, J. Platt, & T. Hoffman (Eds.), Advances in Neural Information Processing Systems 19 (pp. 513-520). Cambridge, MA, USA: MIT Press.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CBCB-3
Abstract
We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is based on the asymptotic distribution of this statistic. The test statistic can be computed in O(m^2) time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.