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Some General Approximation Error and Convergence Rate Estimates in Statistical Learning Theory

  • Saburou Saitoh

Abstract

In statistical learning theory, reproducing kernel Hilbert spaces are used basically as the hypothese space in the approximation of the regression function. In this paper, in connection with a basic formula by S. Smale and D. X. Zhou which is fundamental in the approximation error estimates, we shall give a general formula based on the general theory of reproducing kernels combined with linear mappings in the framework of Hilbert spaces. We shall give a prototype example.

Keywords

learning theory convergence rate approximation reproducing kernel Hilbert space linear mapping inequality 

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References

  1. [1]
    F. Cucker and S. Smale: On the mathematical foundations of learning’, Bull. Amer. Math. Soc. 39 (2001), 1–49.MathSciNetCrossRefGoogle Scholar
  2. [2]
    S. Saitoh: Integral Transforms, Reproducing Kernels and their Applications’, Pitman Res. Notes in Math. Series 369, Addison Wesley Longman, UK, 1997.Google Scholar
  3. [3]
    S. Smale and D. X. Zhou: Estimating the approximation error in learning theory’, Analysis and Applications (to appear).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Saburou Saitoh
    • 1
  1. 1.Department of MathematicsFaculty of Engineering Gunma UniversityKiryuJapan

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