A Kernel Approach to Comparing Distributions

Gretton, A; Borgwardt, KM; Rasch, M; Schölkopf, B; Smola, AJ

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A Kernel Approach to Comparing Distributions

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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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https://www.aaai.org/Papers/AAAI/2007/AAAI07-262.pdf
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Citation

Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., & Smola, A. (2007). A Kernel Approach to Comparing Distributions. In Twenty-Second AAAI Conference on Artificial Intelligence (IAAI-07) (pp. 1637-1641). Menlo Park, CA, USA: AAAI Press.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-CCB1-4

Abstract

We describe a technique for comparing distributions without the need for density estimation as an intermediate step.
Our approach relies on mapping the distributions into a Reproducing Kernel Hilbert Space. We apply this technique to
construct a two-sample test, which is used for determining
whether two sets of observations arise from the same distribution. We use this test in attribute matching for databases using the Hungarian marriage method, where it performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.