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Measuring Statistical Dependence with Hilbert-Schmidt Norms

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83824

Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schoelkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Gretton, A., Bousquet, O., Smola, A., & Schoelkopf, B. (2005). Measuring Statistical Dependence with Hilbert-Schmidt Norms. Algorithmic Learning Theory: 16th International Conference, ALT 2005, 63-78.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D3E5-E
Abstract
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.