A kernel approach to comparing distributions

Authors:
Arthur Gretton;Karsten M. Borgwardt;Malte Rasch;Bernhard Scholköpf;Alexander J. Smola
Affiliations:
MPI for Biological Cybernetics, Tübingen, Germany;Ludwig-Maximilians-Univ., Munich, Germany;Graz Univ. of Technology, Graz, Austria;MPI for Biological Cybernetics, Tübingen, Germany;NICTA, ANU, Canberra, Australia
Venue:
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Year:
2007

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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.