MOTIVATION: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based statistical test for this problem, based on the fact that two distributions are different if and only if there exists at least one function having different expectation on the two distributions. Consequently we use the maximum discrepancy between function means as the basis of a test statistic. The Maximum Mean Discrepancy (MMD) can take advantage of the kernel trick, which allows us to apply it not only to vectors, but strings, sequences, graphs, and other common structured data types arising in molecular biology. RESULTS: We study the practical feasibility of an MMD-based test on three central data integration tasks: Testing cross-platform comparability of microarray data, cancer diagnosis, and data-content based schema matching for two different protein function classification schemas. In all of these experiments, including high-dimensional ones, MMD is very accurate in finding samples that were generated from the same distribution, and outperforms its best competitors. CONCLUSIONS: We have defined a novel statistical test of whether two samples are from the same distribution, compatible with both multivariate and structured data, that is fast, easy to implement, and works well, as confirmed by our experiments. AVAILABILITY: http://www.dbs.ifi.lmu.de/~borgward/MMD.
MOTIVATION: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based statistical test for this problem, based on the fact that two distributions are different if and only if there exists at least one function having different expectation on the two distributions. Consequently we use the maximum discrepancy between function means as the basis of a test statistic. The Maximum Mean Discrepancy (MMD) can take advantage of the kernel trick, which allows us to apply it not only to vectors, but strings, sequences, graphs, and other common structured data types arising in molecular biology. RESULTS: We study the practical feasibility of an MMD-based test on three central data integration tasks: Testing cross-platform comparability of microarray data, cancer diagnosis, and data-content based schema matching for two different protein function classification schemas. In all of these experiments, including high-dimensional ones, MMD is very accurate in finding samples that were generated from the same distribution, and outperforms its best competitors. CONCLUSIONS: We have defined a novel statistical test of whether two samples are from the same distribution, compatible with both multivariate and structured data, that is fast, easy to implement, and works well, as confirmed by our experiments. AVAILABILITY: http://www.dbs.ifi.lmu.de/~borgward/MMD.