id: 05992320
dt: j
an: 05992320
au: Xiang, Dao-Hong; Hu, Ting; Zhou, Ding-Xuan
ti: Learning with varying insensitive loss.
so: Appl. Math. Lett. 24, No. 12, 2107-2109 (2011).
py: 2011
pu: Elsevier Science Ltd. (Pergamon), Oxford
la: EN
cc: 
ut: support vector machine; approximation; regression; reproducing kernel
    Hilbert space
ci: 
li: doi:10.1016/j.aml.2011.06.007
ab: 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.
rv: