Empirical Inference Conference Paper 2008

Nonparametric Independence Tests: Space Partitioning and Kernel Approaches

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
Bibtex Type: Conference Paper (inproceedings)
Address: Berlin, Germany
DOI: 10.1007/978-3-540-87987-9_18
Event Name: 19th International Conference on Algorithmic Learning Theory (ALT08)
Event Place: Budapest, Hungary
Digital: 0
Electronic Archiving: grant_archive
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex

@inproceedings{5375,
  title = {Nonparametric Independence Tests: Space
  Partitioning and Kernel Approaches},
  journal = {Algorithmic Learning Theory: 19th International Conference (ALT08)},
  booktitle = {ALT08},
  abstract = {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.},
  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},
  slug = {5375},
  author = {Gretton, A. and Gy{\"o}rfi, L.},
  month_numeric = {10}
}