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

Dao-Hong Xiang, Ting Hu and Ding-Xuan Zhou

Journal of Applied Mathematics, 2012, vol. 2012, 1-17

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:902139

DOI: 10.1155/2012/902139

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