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A Kernel Method for the Two-Sample-Problem

2007

Conference Paper

ei


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. 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, KM. and Rasch, M. and Schölkopf, B. and Smola, A.
Book Title: Advances in Neural Information Processing Systems 19
Journal: Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference
Pages: 513-520
Year: 2007
Month: September
Day: 0
Editors: B Sch{\"o}lkopf and J Platt and T Hofmann
Publisher: MIT Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 20th Annual Conference on Neural Information Processing Systems (NIPS 2006)
Event Place: Vancouver, BC, Canada

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-19568-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{4193,
  title = {A Kernel Method for the Two-Sample-Problem},
  author = {Gretton, A. and Borgwardt, KM. and Rasch, M. and Sch{\"o}lkopf, B. and Smola, A.},
  journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference},
  booktitle = {Advances in Neural Information Processing Systems 19},
  pages = {513-520},
  editors = {B Sch{\"o}lkopf and J Platt and T Hofmann},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = sep,
  year = {2007},
  month_numeric = {9}
}