On convergence of kernel learning estimators

20th International Conference EURO Mini Conference "Continuous Optimization and Knowledge-Based Technologies", EurOPT 2008

Volumn , Issue , 2008, Pages 306-310

  Norkin, Vladimir I ^a   Keyzer, Michiel A ^b,c  

^a V M GLUSHKOV INSTITUTE OF CYBERNETICS   (Ukraine)

^b BALIKESIR UNIVERSITY   (Turkey)

^c VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Consistency; Ill posedness regularization; Kernel learning; Quantile regression; Stochastic optimization

Indexed keywords

KNOWLEDGE BASED SYSTEMS; PARAMETERIZATION; STOCHASTIC SYSTEMS;

CONSISTENCY; ILL-POSEDNESS; KERNEL LEARNING; QUANTILE REGRESSION; STOCHASTIC OPTIMIZATIONS;

OPTIMIZATION;

EID: 67651226007     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (15)

1. Aronszajn, N. 1950. Theory of reproducing kernels, Transactions of American Mathematical Society 68: 337-404.
2. Bousquet, O. and Elisseeff, A. 2002. Stability and Generalization, Journal of Machine Learning Research 2: 499-526.
3. Cucker, F. and Smale S. 2001. On the mathematial foundations of learning, Bulletin American Mathematical Society 89(1): 1-49.
4. Cucker, F. and Smale, S. 2002. Best choices for regularization parameters in learning theory: on the bias-variance problem, Foundations of Computational Mathematics 2(4): 413-428
5. Ermoliev, Y. M. and Leonardi, G. 1982. Some proposals for stochastic facility location models, Mathematical Modelling 3: 407-420.
6. Györfi, L.; Kohler, M.; Krzy=ak, A., and Walk, H. 2002. A Distribution Free Theory of Nonparametric Regression. Springer.
7. Koenker, R. and Bassett, G. W. 1978. Regression Quantiles, Econometrica 46: 33-50.
8. Poggio, T. and Smale, S. 2003. The mathematics of learning: Dealing with data, Notices of American Mathematical Society 50(5): 537-544.
9. Ruszczynski, A. and Shapiro, A. (eds.). 2003. Stochastic programming. Handbooks in OR & MS, Vol. 10, Elsevier.
10. Schoelkopf, B. and Smola, A. J. 2002. Learning with Kernels. Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, MA.
11. Smale, S.; Yao, Y. 2006. Online Learning Algorithms, Foundations of Computational Mathematics 6(2): 145-170.
12. Smale, S. and Zhou, D. X. 2005. Shannon sampling II: Connections to learning theory, Applied Computational Harmonic Analysis 19(3): 285-302.
13. Takeuchi, I.; Le, Q.V.; Sears, T., and Smola, A. J. 2005. Nonparametric Quantile Estimation, Journal of Machine Learning Research 7: 1001-1033.
14. Tihonov, A. N. and Arsenin, V. Y. 1977. Solution of Ill-Posed Problems. W. H. Winston, Washington DC.
15. Vapnik, V. N. 1998. Statistical Learning Theory. Wiley, New York.