Measuring statistical dependence with Hilbert-Schmidt norms

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3734 LNAI, Issue , 2005, Pages 63-77

  Gretton, Arthur ^a   Bousquet, Olivier ^b   Smola, Alex ^c   Scḧlkopf, Bernhard ^a  

^a MAX PLANCK INSTITUTE FOR BIOLOGICAL CYBERNETICS   (Germany)

^b Pertinence   (France)

^c CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; INDEPENDENT COMPONENT ANALYSIS; MATHEMATICAL OPERATORS;

COVARIANCE OPERATORS; HILBERT-SCHMIDT NORMS; REPRODUCING KERNEL HILBERT SPACES (RKHS); STATISTICAL DEPENDENCE;

STATISTICAL METHODS;

EID: 33646528415     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11564089_7     Document Type: Conference Paper

References (21)

1. S. Achard, D.-T. Pham, and C. Jutten, Quadratic dependence measure for nonlinear blind source separation, 4th International Conference on ICA and BSS, 2003.
2. S.-I. Amari, A. Cichoki, and Yang H., A new learning algorithm for blind signal separation, Advances in Neural Information Processing Systems, vol. 8, MIT Press, 1996, pp. 757-763.
3. F. Bach and M. Jordan, Kernel independent component analysis, Journal of Machine Learning Research 3 (2002), 1-48.
4. C. R. Baker, Joint measures and cross-covariance operators, Transactions of the American Mathematical Society 186 (1973), 273-289.
5. A. Bell and T. Sejnowski, An information-maximization approach to blind separation and blind deconvolution, Neural Computation 7 (1995), no. 6, 1129-1159.
6. J.-F. Cardoso, Blind signal separation: statistical principles, Proceedings of the IEEE 90 (1998), no. 8, 2009-2026.
7. A. Chen and P. Bickel, Consistent independent component analysis and prewhitening, Tech. report, Berkeley, 2004.
8. L. Devroye, L. Györfi, and G. Lugosi, A probabilistic theory of pattern recognition, Applications of mathematics, vol. 31, Springer, New York, 1996.
9. K. Fukumizu, F. R. Bach, and M. I. Jordan, Dimensionality reduction for supervised learning with reproducing kernel hilbert spaces, Journal of Machine Learning Research 5 (2004), 73-99.
10. A. Gretton, R. Herbrich, and A. Smola, The kernel mutual information, Tech. report, Cambridge University Engineering Department and Max Planck Institute for Biological Cybernetics, 2003.
11. A. Gretton, A. Smola, O. Bousquet, R. Herbrich, A. Belitski, M. Augath, Y. Murayama, J. Pauls, B. Schölkopf, and N. Logothetis, Kernel constrained covariance for dependence measurement, AISTATS, vol. 10, 2005.
12. M. Hein and O. Bousquet, Kernels, associated structures, and generalizations, Tech. Report 127, Max Planck Institute for Biological Cybernetics, 2004.
13. W. Hoeffding, Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association 58 (1963), 13-30.
14. A. Hyvärinen, J. Karhunen, and E. Oja, Independent component analysis, John Wiley and Sons, New York, 2001.
15. S. E. Leurgans, R. A. Moyeed, and B. W. Silverman, Canonical correlation analysis when the data are curves, Journal of the Royal Statistical Society, Series B (Methodological) 55 (1993), no. 3, 725-740.
16. E. Miller and J. Fisher III, ICA using spacings estimates of entropy, JMLR 4 (2003), 1271-1295.
17. A. Rényi, On measures of dependence, Acta Math. Acad. Sci. Hungar. 10 (1959), 441-451.
18. A. Samarov and A. Tsybakov, Nonparametric independent component analysis, Bernoulli 10 (2004), 565-582.
19. I. Steinwart, On the influence of the kernel on the consistency of support vector machines, JMLR 2 (2001).
20. Y. Yamanishi, J.-P. Vert, and M. Kanehisa, Heterogeneous data comparison and gene selection with kernel canonical correlation analysis, Kernel Methods in Computational Biology (Cambridge, MA) (B. Schölkopf, K. Tsuda, and J.-P. Vert, eds.), MIT Press, 2004, pp. 209-229.
21. L. Zwald, O. Bousquet, and G. Blanchard, Statistical properties of kernel principal component analysis, Proceedings of the 17th Conference on Computational Learning Theory (COLT), 2004.