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Learning with varying insensitive loss. (English) Zbl 1228.62052
Summary: Support vector machines for regression are implemented based on regularization schemes in reproducing kernel Hilbert spaces associated with an $\epsilon$-insensitive loss. The insensitive parameter $\epsilon >0$ 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 $\epsilon =0$) can be approximated by learning the minimizer of the generalization error with sufficiently small parameter $\epsilon >0$. A concrete learning rate is provided under a regularity condition of the medium function and a noise condition of the probability measure.
##### MSC:
 62G08 Nonparametric regression 46N30 Applications of functional analysis in probability theory and statistics 68T05 Learning and adaptive systems
##### References:
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