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): | Empirical Inference |
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 |
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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}, doi = {10.1007/11564089_7}, month_numeric = {10} } |