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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. 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.
@inproceedings{4193, title = {A Kernel Method for the Two-Sample-Problem}, journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference}, booktitle = {Advances in Neural Information Processing Systems 19}, 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. 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.}, 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}, slug = {4193}, author = {Gretton, A. and Borgwardt, KM. and Rasch, M. and Sch{\"o}lkopf, B. and Smola, A.}, month_numeric = {9} }