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Nonparametric Independence Tests: Space Partitioning and Kernel Approaches

MPG-Autoren
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Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Gretton, A., & Györfi, L. (2008). Nonparametric Independence Tests: Space Partitioning and Kernel Approaches. In Y. Freund, L. Györfi, G. Turán, & T. Zeugmann (Eds.), Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008 (pp. 183-198). Berlin, Germany: Springer.


Zusammenfassung
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, distributionfree
strong consistent tests of independence are derived, as are asymptotically
alpha-level tests. The performance of the tests is evaluated experimentally
on benchmark data.