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Nonparametric Independence Tests: Space Partitioning and Kernel Approaches


Conference Paper


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.

Author(s): Gretton, A. and Györfi, L.
Book Title: ALT08
Journal: Algorithmic Learning Theory: 19th International Conference (ALT08)
Pages: 183-198
Year: 2008
Month: October
Day: 0
Editors: Freund, Y. , L. Gy{\"o}rfi, G. Turán, T. Zeugmann
Publisher: Springer

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1007/978-3-540-87987-9_18
Event Name: 19th International Conference on Algorithmic Learning Theory (ALT08)
Event Place: Budapest, Hungary

Address: Berlin, Germany
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Nonparametric Independence Tests: Space
  Partitioning and Kernel Approaches},
  author = {Gretton, A. and Gy{\"o}rfi, L.},
  journal = {Algorithmic Learning Theory: 19th International Conference (ALT08)},
  booktitle = {ALT08},
  pages = {183-198},
  editors = {Freund, Y. , L. Gy{\"o}rfi, G. Turán, T. Zeugmann},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = oct,
  year = {2008},
  month_numeric = {10}