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Learning Rates of Least-Square Regularized Regression

Learning Rates of Least-Square Regularized Regression This paper considers the regularized learning algorithm associated with the least-square loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and on the capacity of the reproducing kernel Hilbert space measured by covering numbers. When the kernel is C∞ and the regression function lies in the corresponding reproducing kernel Hilbert space, the rate is mζ with ζ arbitrarily close to 1, regardless of the variance of the bounded probability distribution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Foundations of Computational Mathematics Springer Journals

Learning Rates of Least-Square Regularized Regression

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References (33)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Computer Science, general; Math Applications in Computer Science; Linear and Multilinear Algebras, Matrix Theory; Applications of Mathematics; Numerical Analysis
ISSN
1615-3375
eISSN
1615-3383
DOI
10.1007/s10208-004-0155-9
Publisher site
See Article on Publisher Site

Abstract

This paper considers the regularized learning algorithm associated with the least-square loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and on the capacity of the reproducing kernel Hilbert space measured by covering numbers. When the kernel is C∞ and the regression function lies in the corresponding reproducing kernel Hilbert space, the rate is mζ with ζ arbitrarily close to 1, regardless of the variance of the bounded probability distribution.

Journal

Foundations of Computational MathematicsSpringer Journals

Published: Sep 23, 2005

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