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

Haizhang Zhang School of Mathematics and Computational Science, Sun Yat-sen University Jun Zhang University of Michigan

mathscidoc:1609.01003

J Glob Optim, 54, 235–250, 2012
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.
Reproducing kernel Banach spaces · Semi-inner products · Representer theorems·Regularization networks· Support vector machine classification
[ Download ] [ 2016-09-20 18:17:32 uploaded by zhang ] [ 917 downloads ] [ 0 comments ] [ Cited by 10 ] 
@inproceedings{haizhang2012regularized,
  title={Regularized learning in Banach spaces as an optimization problem: representer theorems},
  author={Haizhang Zhang, and Jun Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920181732687289029},
  booktitle={J Glob Optim},
  volume={54},
  pages={235–250},
  year={2012},
}
Haizhang Zhang, and Jun Zhang. Regularized learning in Banach spaces as an optimization problem: representer theorems. 2012. Vol. 54. In J Glob Optim. pp.235–250. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920181732687289029.
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