Shannon sampling II: Connections to learning theory

Applied and Computational Harmonic Analysis

Volumn 19, Issue 3, 2005, Pages 285-302

  Smale, Steve ^a   Zhou, Ding Xuan ^b  

^a TOYOTA TECHNOLOGICAL INSTITUTE AT CHICAGO   (United States)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Frames; Function reconstruction; Learning theory; Reproducing kernel Hilbert space; Shannon sampling

Indexed keywords

ALGORITHMS; PROBABILITY; SAMPLING;

FRAMES; FUNCTION RECONSTRUCTION; SHANNON SAMPLING;

LEARNING SYSTEMS;

EID: 27844555491     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2005.03.001     Document Type: Article

References (18)

1. A. Aldroubi, and K. Gröchenig Non-uniform sampling and reconstruction in shift-invariant spaces SIAM Rev. 43 2001 585 620
2. N. Aronszajn Theory of reproducing kernels Trans. Amer. Math. Soc. 68 1950 337 404
3. F. Cucker, and S. Smale On the mathematical foundations of learning Bull. Amer. Math. Soc. 39 2001 1 49
4. F. Cucker, and S. Smale Best choices for regularization parameters in learning theory Found. Comput. Math. 2 2002 413 428
5. E. De Vito, A. Caponnetto, and L. Rosasco Model selection for regularized least-squares algorithm in learning theory Found. Comput. Math. 5 2005 59 85
6. H.W. Engl, M. Hanke, and A. Neubauer Regularization of Inverse Problems Mathematics and Its Applications vol. 375 1996 Kluwer Academic Dordrecht
7. T. Evgeniou, M. Pontil, and T. Poggio Regularization networks and support vector machines Adv. Comput. Math. 13 2000 1 50
8. C. McDiarmid Concentration Probabilistic Methods for Algorithmic Discrete Mathematics 1998 Springer-Verlag Berlin 195 248
9. P. Niyogi The Informational Complexity of Learning 1998 Kluwer Academic Boston
10. T. Poggio, and S. Smale The mathematics of learning: Dealing with data Notices Amer. Math. Soc. 50 2003 537 544
11. S. Smale, and D.X. Zhou Estimating the approximation error in learning theory Anal. Appl. 1 2003 17 41
12. S. Smale, and D.X. Zhou Shannon sampling and function reconstruction from point values Bull. Amer. Math. Soc. 41 2004 279 305
13. M. Unser Sampling - 50 years after Shannon Proc. IEEE 88 2000 569 587
14. V. Vapnik Statistical Learning Theory 1998 Wiley New York
15. G. Wahba Spline Models for Observational Data 1990 SIAM Philadelphia
16. Y. Ying, McDiarmid inequalities of Bernstein and Bennett forms, Technical Report, City University of Hong Kong, 2004
17. R.M. Young An Introduction to Non-Harmonic Fourier Series 1980 Academic Press New York
18. T. Zhang Leave-one-out bounds for kernel methods Neural Comput. 15 2003 1397 1437