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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Article number902139
Journal / PublicationJournal of Applied Mathematics
Publication statusPublished - 2012



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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