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Regularized learning in Banach spaces as an optimization problem: representer theorems

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  • Haizhang Zhang

    ()

  • Jun Zhang

    ()

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    Abstract

    We view regularized learning of a function in a Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a nondecreasing regularizer. When the loss function and the regularizer are differentiable, a characterization equation for the minimizer is also established. Copyright Springer Science+Business Media, LLC. 2012

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    File URL: http://hdl.handle.net/10.1007/s10898-010-9575-z
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    Bibliographic Info

    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 54 (2012)
    Issue (Month): 2 (October)
    Pages: 235-250

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    Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:235-250

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    Web page: http://www.springer.com/business/operations+research/journal/10898

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    Related research

    Keywords: Reproducing kernel Banach spaces; Semi-inner products; Representer theorems; Regularization networks; Support vector machine classification;

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