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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 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.
MSC:
62G08Nonparametric regression
46N30Applications of functional analysis in probability theory and statistics
68T05Learning and adaptive systems
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