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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| 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. |
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| ISSN: | 1110-757X 1687-0042 |