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}
}