PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Consistent Nonparametric Tests of Independence
Arthur Gretton and Laszlo Gyorfi
Journal of Machine Learning Research Volume 11, pp. 1391-1423, 2010. ISSN 1533-7928

Abstract

Three simple and explicit procedures for testing the independence of twomulti-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. Two kinds of tests are provided. Distribution free strong consistent tests are derived on the basis of large deviation bounds on the test statistics: these testsmake almost surely no Type I or Type II error after a random sample size. Asymptotically alpha-level tests are obtained from the limiting distribution of the test statistics. For the latter tests, the Type I error converges to a fixed non-zero value alpha, and the Type II error drops to zero, for increasing sample size. All tests reject the null hypothesis of independence if the test statistics become large. The performance of the tests is evaluated experimentally on benchmark data.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:7077
Deposited By:Andras Gyorgy
Deposited On:01 March 2011