PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A Kernel Method for the Two-Sample-Problem
Arthur Gretton, K Borgwardt, M Rasch, Bernhard Schölkopf and Alex Smola
In: NIPS 2006, 04-09 December 2006, Vancouver Canada.


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: we obtain better performance than alternative tests on high dimensional multivariate data. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.

EPrint Type:Conference or Workshop Item (Oral)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:2389
Deposited By:Arthur Gretton
Deposited On:22 November 2006