Learning with varying insensitive loss

Support vector machines for regression are implemented based on regularization schemes in reproducing kernel Hilbert spaces associated with an ϵ -insensitive loss. The insensitive parameter ϵ > 0 changes with the sample size and plays a crucial role in the learning algorithm. The purpose of this paper is to present a perturbation theorem to show how the medium function of the probability measure for regression (with ϵ = 0 ) can be approximated by learning the minimizer of the generalization error with sufficiently small parameter ϵ > 0 . A concrete learning rate is provided under a regularity condition of the medium function and a noise condition of the probability measure.