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 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. copyright © 2012 dao-hong xiang et al.