Nonparametric independence tests: space partitioning and kernel approaches
Arthur Gretton and Laszlo Gyorfi
19th International Conference on Algorithmic Learning Theory, ALT 2008, Proceedings
Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence
, Berlin, Heidelberg, Germany
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.