The covering number in learning theory

Journal of Complexity

Volumn 18, Issue 3, 2002, Pages 739-767

  Zhou, Ding Xuan ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Covering number; Learning theory; Mercer kernel; Reproducing kernel Hilbert space

Indexed keywords

EID: 0036748375     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.2002.0635     Document Type: Article

References (13)

1. N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337-404.
2. F. Cucker and S. Smale, On the mathematical foundations of learning, Soc. 39 (2001), 1-49.
3. D. Edmunds and H. Triebel, "Function Spaces, Entropy Numbers, Cambridge Univ. Press, Cambridge, UK, 1996.
4. T. Evgeniou, M. Pontil, and T. Poggio, Regularization networks and machines, Adv. Comput. Math. 13 (2000), 1-50.
5. Y. Guo, P. L. Bartlett, J. Shawe-Taylor, and R. C. Williamson, Covering support vector machines, in "Proceedings of the Twelfth Annual Computational Learning Theory," pp. 267-277, Assoc. Comput. Mac., New York, 1999.
6. P. Niyogi, "The Informational Complexity of Learning," Kluwer Academic, 1998.
7. M. Pontil, A note on different covering numbers in Learning Theory, preprint, 2001.
8. R. Schaback, Reconstruction of multivariate functions from scattered manuscript, 1997.
9. S. Smale, private communications, 2000-2001.
10. S. Smale and D. X. Zhou, Estimating the approximation error in learning Appl., to appear.
11. V. Vapnik, "Statistical Learning Theory," Wiley, New York, 1998.
12. R. C. Williamson, A. J. Smola, and B. Schölkopf, Generalization regularization networks and support vector machines via entropy numbers operators, IEEE Trans. Inform. Theory, to appear.
13. Z. Wu and R. Schaback, Local error estimates for radial basis function scattered data, IMA J. Numer. Anal. 13 (1993), 13-27.