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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/902139 |
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| _version_ | 1849695910302318592 |
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| author | Dao-Hong Xiang Ting Hu Ding-Xuan Zhou |
| author_facet | Dao-Hong Xiang Ting Hu Ding-Xuan Zhou |
| author_sort | Dao-Hong Xiang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d092a630f3b841e8b1b2dd95982d0604 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d092a630f3b841e8b1b2dd95982d06042025-08-20T03:19:37ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/902139902139Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile RegressionDao-Hong Xiang0Ting Hu1Ding-Xuan Zhou2Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaDepartment of Mathematics, City University of Hong Kong, Kowloon, Hong KongWe 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.http://dx.doi.org/10.1155/2012/902139 |
| spellingShingle | Dao-Hong Xiang Ting Hu Ding-Xuan Zhou Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression Journal of Applied Mathematics |
| title | Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression |
| title_full | Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression |
| title_fullStr | Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression |
| title_full_unstemmed | Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression |
| title_short | Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression |
| title_sort | approximation analysis of learning algorithms for support vector regression and quantile regression |
| url | http://dx.doi.org/10.1155/2012/902139 |
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