Measuring Statistical Dependence with Hilbert-Schmidt Norms


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 HSIC 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.

DOI: 10.1007/11564089_7

Extracted Key Phrases

2 Figures and Tables

Citations per Year

515 Citations

Semantic Scholar estimates that this publication has 515 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{Gretton2005MeasuringSD, title={Measuring Statistical Dependence with Hilbert-Schmidt Norms}, author={Arthur Gretton and Olivier Bousquet and Alexander J. Smola and Bernhard Sch{\"{o}lkopf}, booktitle={ALT}, year={2005} }