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

Abstract EN

We study learning algorithms generated by regularization schemes in reproducingkernel Hilbert spaces associated with an ϵ-insensitive pinball loss.

This lossfunction is motivated by the ϵ-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.