Analysis of support vector machines regression

Foundations of Computational Mathematics

Volumn 9, Issue 2, 2009, Pages 243-257

  Tong, Hongzhi ^a   Chen, Di Rong ^b   Peng, Lizhong ^b  

^a PEKING UNIVERSITY   (China)

^b BEIHANG UNIVERSITY   (China)

Author keywords

Excess error; Learning rates; Regularization; Reproducing kernel Hilbert spaces; Support vector machines regression

Indexed keywords

CLASSIFICATION ALGORITHM; ITERATION TECHNIQUES; LEARNING RATES; LEAST SQUARE REGRESSION; QUANTITATIVE ESTIMATES; REGULARIZATION; REPRODUCING KERNEL HILBERT SPACES; SUPPORT VECTOR MACHINES REGRESSION;

LEARNING ALGORITHMS; REGRESSION ANALYSIS; SUPPORT VECTOR MACHINES;

ITERATIVE METHODS;

EID: 62949199060     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-008-9026-0     Document Type: Article

References (25)

1. N. Aronszajn 1950 Theory of reproducing kernels Trans. Am. Math. Soc. 68 337 404
2. P.L. Bartlett 1998 The sample complexity of pattern classification with neural networks: The size of the weights is more import than the size of the network IEEE Trans. Inf. Theory 44 525 536
3. O. Bousquet A. Elisseeff 2002 Stability and generalization J. Mach. Learn. Res. 2 499 526
4. D.R. Chen Q. Wu Y. Ying D.X. Zhou 2004 Support vector machine soft margin classifiers: error analysis J. Mach. Learn. Res. 5 1143 1175
5. A. Christmann I. Steinwart 2007 Consistency and robustness of kernel-based regression in convex risk minimization Bernoulli 13 799 819
6. F. Cucker S. Smale 2001 On the mathematical foundations of learning theory Bull. Am. Math. Soc. 39 1 49
7. F. Cucker S. Smale 2002 Best choices for regularization parameters in learning theory: On the bias-variance problem Found. Comput. Math. 2 413 428
8. E. De Vito A. Caponnetto L. Rosasco 2005 Model selection for regularized least-squares algorithm in learning theory Found. Comput. Math. 5 59 85
9. L. Devroye, L. Györfi, G. Lugosi, A Probabilistic Theory of Pattern Recognition (Springer, New York, 1997).
10. T. Evgeniou M. Pontil T. Poggio 2000 Regularization networks and support vector machines Adv. Comput. Math. 13 1 50
11. P.J. Huber, Robust Statistics (Wiley, New York, 1981).
12. T. Poggio S. Smale 2003 The mathematics of learning: Deal with data Not. Am. Math. Soc. 50 537 544
13. M. Pontil, S. Mukherjee, F. Girosi, On the noise model of support vector machine regression, A.I. Memo 1651, MIT Artificial Intelligence Lab., 1998.
14. L. Rosasco E. De Vito A. Caponnetto M. Piana A. Verri 2004 Are loss functions all the same? Neural Comput. 16 1063 1076
15. B. Scholkopf, A.J. Smola, Learning with Kernel (MIT Press, Cambridge, 2002).
16. S. Smale D.X. Zhou 2005 Shannon sampling II. Connections to learning theory Appl. Comput. Harmon. Anal. 19 285 302
17. S. Smale D.X. Zhou 2007 Learning theory estimates via integral operators and their applications Constr. Approx. 26 153 172
18. C. Scovel, I. Steinwart, Fast rates for support vector machine, in Proceedings of the Conference on Learning Theory (COLT-2005), pp. 279-294.
19. V. Vapnik, The Nature of Statistical Learning Theory (Springer, New York, 1995).
20. V. Vapnik, Statistical Learning Theory (Wiley, New York, 1998).
21. Q. Wu D.X. Zhou 2005 SVM soft margin classifiers: Linear programming versus quadratic programming Neural Comput. 17 1160 1187
22. Q. Wu Y. Ying D.X. Zhou 2006 Learning rates of least-square regularized regression Found. Comput. Math. 6 171 192
23. D.X. Zhou 2002 The covering number in learning theory J. Complex. 18 739 767
24. D.X. Zhou 2003 Capacity of reproducing kernel spaces in learning theory IEEE Trans. Inf. Theory 49 1743 1752
25. D.X. Zhou K. Jetter 2006 Approximation with polynomial kernels and SVM classifiers Adv. Comput. Math. 25 323 344