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

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Functional Equations, Inequalities and Applications
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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.

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References

  1. F. Cucker and S. Smale: On the mathematical foundations of learning’, Bull. Amer. Math. Soc. 39 (2001), 1–49.

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  2. S. Saitoh: Integral Transforms, Reproducing Kernels and their Applications’, Pitman Res. Notes in Math. Series 369, Addison Wesley Longman, UK, 1997.

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  3. S. Smale and D. X. Zhou: Estimating the approximation error in learning theory’, Analysis and Applications (to appear).

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© 2003 Springer Science+Business Media Dordrecht

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Saitoh, S. (2003). Some General Approximation Error and Convergence Rate Estimates in Statistical Learning Theory. In: Rassias, T.M. (eds) Functional Equations, Inequalities and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0225-6_11

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  • DOI: https://doi.org/10.1007/978-94-017-0225-6_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6406-6

  • Online ISBN: 978-94-017-0225-6

  • eBook Packages: Springer Book Archive

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