PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Nonparametric independence tests: space partitioning and kernel approaches
Arthur Gretton and Laszlo Gyorfi
In: 19th International Conference on Algorithmic Learning Theory, ALT 2008, Proceedings Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence , 5254 . (2008) Springer-Verlag , Berlin, Heidelberg, Germany , pp. 183-198. ISBN 978-3-540-87986-2


Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L-1, 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 alpha-level tests. The performance of the tests is evaluated experimentally on benchmark data.

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EPrint Type:Book Section
Additional Information:(Budapest, Hungary, Oct 13-16, 2008)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:5018
Deposited By:Laszlo Gyorfi
Deposited On:18 March 2009