Learning in Hilbert vs. Banach spaces: A measure embedding viewpoint

Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Volumn , Issue , 2011, Pages

  Sriperumbudur, Bharath K ^a   Fukumizu, Kenji ^b   Lanckriet, Gert R G ^c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BANACH SPACES; COMPUTATIONAL EFFICIENCY; LEARNING ALGORITHMS; VECTOR SPACES;

DISTANCE MEASURE; EMBEDDING PROBABILITY; EMBEDDINGS; GENERALISATION; HILBERT; HILBERT METHODS; PARZEN WINDOWS CLASSIFIERS; PROBABILITY MEASURES; REPRODUCING KERNEL BANACH SPACES; SIMPLE++;

HILBERT SPACES;

EID: 85162378822     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68:337-404, 1950.
2. B. Beauzamy. Introduction to Banach spaces and their Geometry. North-Holland, The Netherlands, 1985.
3. K. Bennett and E. Bredensteiner. Duality and geometry in svm classifier. In Proc. 17th International Conference on Machine Learning, pages 57-64, 2000.
4. A. Berlinet and C. Thomas-Agnan. Reproducing Kernel Hilbert Spaces in Probability and Statistics. Kluwer Academic Publishers, London, UK, 2004.
5. R. Der and D. Lee. Large-margin classification in Banach spaces. In JMLR Workshop and Conference Proceedings, volume 2, pages 91-98. AISTATS, 2007.
6. K. Fukumizu, F. R. Bach, and M. I. Jordan. Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces. Journal of Machine Learning Research, 5:73-99, 2004.
7. K. Fukumizu, A. Gretton, X. Sun, and B. Schölkopf. Kernel measures of conditional dependence. In J.C. Platt, D. Koller, Y. Singer, and S. Roweis, editors, Advances in Neural Information Processing Systems 20, pages 489-496, Cambridge, MA, 2008. MIT Press.
8. J. R. Giles. Classes of semi-inner-product spaces. Trans. Amer. Math. Soc., 129:436-446, 1967.
9. A. Gretton, K.M. Borgwardt,M. Rasch, B. Schölkopf, and A. Smola. A kernel method for the two sample problem. In B. Schölkopf, J. Platt, and T. Hoffman, editors, Advances in Neural Information Processing Systems 19, pages 513-520. MIT Press, 2007.
10. A. Gretton, K. Fukumizu, C. H. Teo, L. Song, B. Schölkopf, and A. J. Smola. A kernel statistical test of independence. In J. Platt, D. Koller, Y. Singer, and S. Roweis, editors, Advances in Neural Information Processing Systems 20, pages 585-592. MIT Press, 2008.
11. M. Hein, O. Bousquet, and B. Schölkopf. Maximal margin classification for metric spaces. J. Comput. System Sci., 71:333-359, 2005.
12. G. Lumer. Semi-inner-product spaces. Trans. Amer. Math. Soc., 100:29-43, 1961.
13. C. A. Micchelli and M. Pontil. A function representation for learning in Banach spaces. In Conference on Learning Theory, 2004.
14. B. Schölkopf and A. J. Smola. Learning with Kernels. MIT Press, Cambridge, MA, 2002.
15. J. Shawe-Taylor and N. Cristianini. Kernel Methods for Pattern Analysis. Cambridge University Press, UK, 2004.
16. A. J. Smola, A. Gretton, L. Song, and B. Schölkopf. A Hilbert space embedding for distributions. In Proc. 18th International Conference on Algorithmic Learning Theory, pages 13-31. Springer-Verlag, Berlin, Germany, 2007.
17. K. Sridharan and A. Tewari. Convex games in Banach spaces. In Conference on Learning Theory, 2010.
18. B. K. Sriperumbudur, K. Fukumizu, A. Gretton, G. R. G. Lanckriet, and B. Schölkopf. Kernel choice and classifiability for RKHS embeddings of probability distributions. In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I.Williams, and A. Culotta, editors, Advances in Neural Information Processing Systems 22, pages 1750-1758. MIT Press, 2009.
19. B. K. Sriperumbudur, A. Gretton, K. Fukumizu, G. R. G. Lanckriet, and B. Schölkopf. Injective Hilbert space embeddings of probability measures. In R. Servedio and T. Zhang, editors, Proc. of the 21st Annual Conference on Learning Theory, pages 111-122, 2008.
20. B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G. R. G. Lanckriet. Hilbert space embeddings and metrics on probability measures. Journal of Machine Learning Research, 11:1517-1561, 2010.
21. p-coefficient regularization. Neural Computation, 22:3221-3235, 2010.
22. U. von Luxburg and O. Bousquet. Distance-based classification with Lipschitz functions. Journal for Machine Learning Research, 5:669-695, 2004.
23. H. Wendland. Scattered Data Approximation. Cambridge University Press, Cambridge, UK, 2005.
24. H. Zhang, Y. Xu, and J. Zhang. Reproducing kernel Banach spaces for machine learning. Journal of Machine Learning Research, 10:2741-2775, 2009.