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A Kernel Method for the Two-Sample-Problem




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. We show that 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.

Author(s): Gretton, A. and Borgwardt, K. and Rasch, M. and Schölkopf, B. and Smola, A.
Year: 2006
Month: December
Day: 0

Department(s): Empirical Inference
Bibtex Type: Talk (talk)

Digital: 0
Event Name: 20th Annual Conference on Neural Information Processing Systems (NIPS 2006)
Event Place: Vancouver, BC, Canada
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {A Kernel Method for the Two-Sample-Problem},
  author = {Gretton, A. and Borgwardt, K. and Rasch, M. and Sch{\"o}lkopf, B. and Smola, A.},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = dec,
  year = {2006},
  month_numeric = {12}