@inproceedings{3774,
  title = {Measuring Statistical Dependence with Hilbert-Schmidt Norms},
  journal = {Algorithmic Learning Theory: 16th International Conference, ALT 2005},
  booktitle = {Algorithmic Learning Theory, Lecture Notes in Computer Science, Vol. 3734},
  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.},
  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},
  slug = {3774},
  author = {Gretton, A. and Bousquet, O. and Smola, A. and Schoelkopf, B.},
  month_numeric = {10}
}