Empirical Inference Talk 2006

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
Bibtex Type: Talk (talk)
Digital: 0
Electronic Archiving: grant_archive
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:

BibTex

@talk{4275,
  title = {A Kernel Method for the Two-Sample-Problem},
  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.  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.},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = dec,
  year = {2006},
  slug = {4275},
  author = {Gretton, A. and Borgwardt, K. and Rasch, M. and Sch{\"o}lkopf, B. and Smola, A.},
  month_numeric = {12}
}