Least square regression with indefinite kernels and coefficient regularization

Applied and Computational Harmonic Analysis

Volumn 30, Issue 1, 2011, Pages 96-109

  Sun, Hongwei ^a   Wu, Qiang ^b  

^a UNIVERSITY OF JINAN   (China)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Capacity independent error bounds; Coefficient regularization; Indefinite kernel; Integral operator; Learning rates; Least square regression; Mercer kernel

Indexed keywords

COEFFICIENT REGULARIZATION; ERROR BOUND; INDEFINITE KERNEL; INTEGRAL OPERATORS; LEARNING RATES; LEAST SQUARE REGRESSION; MERCER KERNEL;

ERROR ANALYSIS; REGRESSION ANALYSIS; SAMPLING;

MATHEMATICAL OPERATORS;

EID: 78649308061     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2010.04.001     Document Type: Article

References (30)

1. N. Aronszajn Theory of reproducing kernels Trans. Amer. Math. Soc. 68 1950 337 404
2. F. Bauer, S. Pereverzev, and L. Rosasco On regularization algorithms in learning theory J. Complexity 23 2007 52 72
3. A. Cannon, J.M. Ettinger, D. Hush, and C. Scovel Machine learning with data dependent hypothesis classes J. Mach. Learn. Res. 2 2002 335 358
4. F. Cucker, and S. Smale On the mathematical foundations of learning Bull. Amer. Math. Soc. 39 2001 1 49
5. F. Cucker, and S. Smale Best choices for regularization parameters in learning theory: on the bias-variance problem Found. Comput. Math. 2 2002 413 428
6. T. Evgeniou, M. Pontil, and T. Poggio Regularization networks and support vector machines Adv. Comput. Math. 13 2000 1 50
7. G.R.G. Lanckriet, N. Cristianini, P. Bartlett, L. El Ghaoui, and M.I. Jordan Learning the kernel matrix with semidefinite programming J. Mach. Learn. Res. 5 2004 27 72 (electronic)
8. C. Liu Gabor-based kernel PCA with fractional power polynomial models for face recognition IEEE Trans. Pattern Anal. Mach. Intell. 26 2004 572 581
9. L. Lo Gerfo, L. Rosasco, F. Odone, E. De Vito, and A. Verri Spectral algorithms for supervised learning Neural Comput. 20 2008 1873 1897
10. R. Luss, and A. d'Aspremont Support vector machine classification with indefinite kernels Math. Program. Comput. 1 2009 97 118
11. C.A. Micchelli, and M. Pontil Learning the kernel function via regularization J. Mach. Learn. Res. 6 2005 1099 1125 (electronic)
12. T. Poggio, and S. Smale The mathematics of learning: dealing with data Notices Amer. Math. Soc. 50 2003 537 544
13. H. Saigo, J. Vert, N. Ueda, and T. Akutsu Protein homology detection using string alignment kernels Bioinformatics 20 2004 1682 1689
14. B. Scholkopf, and A. Smola Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond 2002 MIT Press
15. S. Smale, and D.-X. Zhou Shannon sampling and function reconstruction from point values Bull. Amer. Math. Soc. (N.S.) 41 2004 279 305 (electronic)
16. S. Smale, and D.-X. Zhou Shannon sampling. II. Connections to learning theory Appl. Comput. Harmon. Anal. 19 2005 285 302
17. S. Smale, and D.X. Zhou Learning theory estimates via integral operators and their approximations Constr. Approx. 26 2007 153 172
18. H. Sun, and Q. Wu Regularized least square regression with dependent samples Adv. Comput. Math. 32 2 2010 175 189 10.1007/s10444-008-9099-y
19. H. Sun, and Q. Wu Application of integral operator for regularized least square regression Math. Comput. Modelling 49 2009 276 285
20. S. Sun, and Q. Wu A note on application of integral operator in learning theory Appl. Comput. Harmon. Anal. 26 2009 416 421
21. V. Vapnik Statistical Learning Theory 1998 Wiley New York
22. Q. Wu, Y. Ying, and D.X. Zhou Learning rates of least-square regularized regression Found. Comput. Math. 6 2006 171 192
23. Q. Wu, Y. Ying, and D.-X. Zhou Multi-kernel regularized classifiers J. Complexity 23 2007 108 134
24. Q. Wu, and D.-X. Zhou SVM soft margin classifiers: linear programming versus quadratic programming Neural Comput. 17 2005 1160 1187
25. Q. Wu, and D.-X. Zhou Learning with sample dependent hypothesis spaces Comput. Math. Appl. 56 2008 2896 2907
26. Q.W. Xiao, D.X. Zhou, Learning by nonsymmetric kernels with data dependent spaces and ℓ 1 -regularizer, preprint.
27. Y. Xu, and H. Zhang Refinable kernels J. Mach. Learn. Res. 8 2007 2083 2120
28. Y. Xu, and H. Zhang Refinement of reproducing kernels J. Mach. Learn. Res. 10 2009 107 140
29. T. Zhang Leave-one-out bounds for kernel methods Neural Comput. 15 2003 1397 1437
30. T. Zhang Learning bounds for kernel regression using effective data dimensionality Neural Comput. 17 2005 2077 2098