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

[摘要] We study learning algorithms generated by regularization schemes in reproducingkernel Hilbert spaces associated with anϵ-insensitive pinball loss. This lossfunction is motivated by theϵ-insensitive loss for support vector regression and thepinball loss for quantile regression. Approximation analysis is conducted for thesealgorithms by means of a variance-expectation bound when a noise condition issatisfied for the underlying probability measure. The rates are explicitly derivedunder a priori conditions on approximation and capacity of the reproducing kernelHilbert space. As an application, we get approximation orders for the supportvector regression and the quantile regularized regression.

[学科分类] 应用数学