On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Measuring statistical dependence with hilbert-schmidt norms
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
On the asymptotic properties of a nonparametric L1-test statistic of homogeneity
IEEE Transactions on Information Theory
Consistent Nonparametric Tests of Independence
The Journal of Machine Learning Research
Efficient Heuristics for Discriminative Structure Learning of Bayesian Network Classifiers
The Journal of Machine Learning Research
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Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. All tests reject the null hypothesis of independence if the test statistics become large. The large deviation and limit distribution properties of all three test statistics are given. Following from these results, distribution-free strong consistent tests of independence are derived, as are asymptotically 茂戮驴-level tests. The performance of the tests is evaluated experimentally on benchmark data.