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2012 Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression
Dao-Hong Xiang, Ting Hu, Ding-Xuan Zhou
J. Appl. Math. 2012: 1-17 (2012). DOI: 10.1155/2012/902139

Abstract

We study learning algorithms generated by regularization schemes in reproducing kernel Hilbert spaces associated with an {\epsilon} -insensitive pinball loss. This loss function is motivated by the {\epsilon} -insensitive loss for support vector regression and the pinball loss for quantile regression. Approximation analysis is conducted for these algorithms by means of a variance-expectation bound when a noise condition is satisfied for the underlying probability measure. The rates are explicitly derived under a priori conditions on approximation and capacity of the reproducing kernel Hilbert space. As an application, we get approximation orders for the support vector regression and the quantile regularized regression.

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Dao-Hong Xiang. Ting Hu. Ding-Xuan Zhou. "Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression." J. Appl. Math. 2012 1 - 17, 2012. https://doi.org/10.1155/2012/902139

Information

Published: 2012
First available in Project Euclid: 17 October 2012

zbMATH: 1235.68206
MathSciNet: MR2880823
Digital Object Identifier: 10.1155/2012/902139

Rights: Copyright © 2012 Hindawi

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