Nonparametric independence tests: Space partitioning and Kernel approaches

Arthur Gretton, László Györfi

Research output: Contribution to journalConference article

4 Citations (Scopus)


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 α-level tests. The performance of the tests is evaluated experimentally on benchmark data.

Original languageEnglish
Pages (from-to)183-198
Number of pages16
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5254 LNAI
Publication statusPublished - Dec 1 2008
Event19th International Conference on Algorithmic Learning Theory, ALT 2008 - Budapest, Hungary
Duration: Oct 13 2008Oct 16 2008

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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