A Hilbert Space Embedding for Distributions

  • Authors:
  • Alex Smola;Arthur Gretton;Le Song;Bernhard Schölkopf

  • Affiliations:
  • National ICT Australia, North Road, Canberra 0200 ACT, Australia;MPI for Biological Cybernetics, Spemannstr. 38, 72076 Tübingen, Germany;National ICT Australia, North Road, Canberra 0200 ACT, Australia;MPI for Biological Cybernetics, Spemannstr. 38, 72076 Tübingen, Germany

  • Venue:
  • ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
  • 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. Applications of this technique can be found in two-sample tests, which are used for determining whether two sets of observations arise from the same distribution, covariate shift correction, local learning, measures of independence, and density estimation.