id: 05851713
dt: a
an: 05851713
au: Wu, Qiang; Ying, Yiming; Zhou, Ding-Xuan
ti: Learning theory: from regression to classification.
so: Jetter, Kurt (ed.) et al., Topics in multivariate approximation and
    interpolation. Amsterdam: Elsevier (ISBN 978-0-444-51844-6). Studies in
    Computational Mathematics 12, 257-290 (2005).
py: 2005
pu: Amsterdam: Elsevier
la: EN
cc: 
ut: 
ci: Zbl 1205.41002
li: doi:10.1016/S1570-579X(06)80011-X
ab: Summary: We give a brief survey of regularization schemes in learning
    theory for the purposes of regression and classification, from an
    approximation theory point of view. First, the classical method of
    empirical risk minimization is reviewed for regression with a general
    convex loss function. Next, we explain ideas and methods for the error
    analysis of regression algorithms generated by Tikhonov regularization
    schemes associated with reproducing kernel Hilbert spaces. Then binary
    classification algorithms given by regularization schemes are described
    with emphasis on support vector machines and noise conditions for
    distributions. Finally, we mention further topics and some open
    problems in learning theory. For the entire collection, see [{\it K.
    Jetter} (ed.), {\it M. Buhmann} (ed.), {\it W. Haussmann} (ed.), {\it
    R. Schaback} (ed.), {\it J. Stoeckler (ed.)}, Topics in multivariate
    approximation and interpolation. Studies in Computational Mathematics
    12. Amsterdam: Elsevier. (2005; Zbl 1205.41002)].
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