Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression
Dao-Hong Xiang, Ting Hu, Ding‐Xuan Zhou · Journal of Applied Mathematics · 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.