Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression

We study learning algorithms generated by regularization schemes in reproducing kernel Hilbert spaces associated with an ϵ-insensitive pinball loss. This loss function is motivated by the ϵ-insensitive loss for support vector regression and the pinball loss for quantile regression. Approximation ana...

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Bibliographic Details
Main Authors: Dao-Hong Xiang, Ting Hu, Ding-Xuan Zhou
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/902139
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Summary:We study learning algorithms generated by regularization schemes in reproducing kernel Hilbert spaces associated with an ϵ-insensitive pinball loss. This loss function is motivated by the ϵ-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.
ISSN:1110-757X
1687-0042