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Measuring Statistical Dependence with Hilbert-Schmidt Norms

2005

Conference Paper

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We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on {methodname} do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

Author(s): Gretton, A. and Bousquet, O. and Smola, A. and Schoelkopf, B.
Book Title: Algorithmic Learning Theory, Lecture Notes in Computer Science, Vol. 3734
Journal: Algorithmic Learning Theory: 16th International Conference, ALT 2005
Pages: 63-78
Year: 2005
Month: October
Day: 8
Editors: S Jain and H-U Simon and E Tomita
Publisher: Springer

Department(s): Empirische Inferenz
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1007/11564089_7
Event Name: 16th International Conference ALT 2005
Event Place: Singapore

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

Links: PDF

BibTex

@inproceedings{3774,
  title = {Measuring Statistical Dependence with Hilbert-Schmidt Norms},
  author = {Gretton, A. and Bousquet, O. and Smola, A. and Schoelkopf, B.},
  journal = {Algorithmic Learning Theory: 16th International Conference, ALT 2005},
  booktitle = {Algorithmic Learning Theory, Lecture Notes in Computer Science, Vol. 3734},
  pages = {63-78},
  editors = {S Jain and H-U Simon and E Tomita},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = oct,
  year = {2005},
  month_numeric = {10}
}