Special Issue on Approximation Theory in Commemoration of Professor Yongsheng SunNo Access

LEARNING RATES OF REGULARIZED REGRESSION FOR FUNCTIONAL DATA

YONG-LI XU

Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, Beijing, 100091, P. R. China

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and

DI-RONG CHEN

Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, Beijing, 100091, P. R. China

Corresponding author.

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https://doi.org/10.1142/S0219691309003288Cited by:6 (Source: Crossref)

Abstract

The study of regularized learning algorithms is a very important issue and functional data analysis extends classical methods. We establish the learning rates of the least square regularized regression algorithm in reproducing kernel Hilbert space for functional data. With the iteration method, we obtain fast learning rate for functional data. Our result is a natural extension for least square regularized regression algorithm when the dimension of input data is finite.

In commemoration of the 80th birthday anniversary of Professor Yongsheng Sun

Keywords:

AMSC: 62J02, 68T05

References

O. Bousquet and A. Elisseef, J. Mach. Learn. Res. 2, 499 (2002), DOI: 10.1162/153244302760200704. Web of Science, Google Scholar
A. Caponnetto and E. de Vito, Fast rates for regularized least-squares algorithm, Technical Report 248/AI Memo 2005-013, CBCL, Massachusetts Institute of Technology (2005) . Google Scholar
F. Cucker and S. Smale, Bull. Amer. Math. Soc. 39, 1 (2001), DOI: 10.1090/S0273-0979-01-00923-5. Crossref, Web of Science, Google Scholar
F. Cucker and S. Smale, Found. Comput. Math. 2, 413 (2002), DOI: 10.1007/s102080010030. Crossref, Web of Science, Google Scholar
F. Cucker and D. X. Zhou , Learning Theory: An Approximation Theory Viewpoint ( Cambridge Univ. Press , 2007 ) . Crossref, Google Scholar
T. Evgeniou, M. Pontil and T. Poggio, Adv. Comput. Math. 13, 1 (2000), DOI: 10.1023/A:1018946025316. Crossref, Web of Science, Google Scholar
F. Ferraty and P. Vieu , Nonparametric Functional Data Analysis: Theory and Practice , Springer Series in Statistics ( Springer , 2006 ) . Google Scholar
N. Hernándezet al., Analytica Chimica Acta 642, 110 (2009). Crossref, Web of Science, Google Scholar
S. Mukherjeeet al., Adv. Comput. Math. 25, 161 (2006), DOI: 10.1007/s10444-004-7634-z. Crossref, Web of Science, Google Scholar
C. Preda, J. Statist. Plann. Inference 137, 829 (2007), DOI: 10.1016/j.jspi.2006.06.011. Crossref, Web of Science, Google Scholar
F. Rossi and B. Conan-Guezs, Neural Networks 18, 45 (2005), DOI: 10.1016/j.neunet.2004.07.001. Crossref, Web of Science, Google Scholar
J. O. Ramsay and B. W. Silverman , Functional Data Analysis , 2nd edn. ( Springer , New York , 2005 ) . Crossref, Google Scholar
S. Smale and D. X. Zhou, Appl. Comput. Harmon. Anal. 19, 285 (2005), DOI: 10.1016/j.acha.2005.03.001. Crossref, Web of Science, Google Scholar
S. Smale and D. X. Zhou, Const. Approx. 26, 153 (2007), DOI: 10.1007/s00365-006-0659-y. Crossref, Web of Science, Google Scholar
I. Steinwart and C. Scovel, Fast rates for support vector machines, Proceedings of the 18th Conference on Learning Theory, COLT 2005 (Springer, 2005) pp. 279–294. Google Scholar
Q. Wu, Y. M. Ying and D. X. Zhou, Found. Comput. Math. 6, 171 (2006), DOI: 10.1007/s10208-004-0155-9. Crossref, Web of Science, Google Scholar
Y.-L. Xu and D.-R. Chen, J. Statist. Plann. Inference 7, 2180 (2008). Google Scholar