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On Stochastic Optimization and Statistical Learning in Reproducing Kernel Hilbert Spaces by Support Vector Machines (SVM)
Volume 20, Issue 2 (2009), pp. 273–292
Vladimir Norkin   Michiel Keyzer  

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https://doi.org/10.15388/Informatica.2009.250
Pub. online: 1 January 2009      Type: Research Article     

Received
1 August 2008
Accepted
1 February 2009
Published
1 January 2009

Abstract

The paper studies stochastic optimization problems in Reproducing Kernel Hilbert Spaces (RKHS). The objective function of such problems is a mathematical expectation functional depending on decision rules (or strategies), i.e. on functions of observed random parameters. Feasible rules are restricted to belong to a RKHS. This kind of problems arises in on-line decision making and in statistical learning theory. We solve the problem by sample average approximation combined with Tihonov's regularization and establish sufficient conditions for uniform convergence of approximate solutions with probability one, jointly with a rule for downward adjustment of the regularization factor with increasing sample size.

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Keywords
stochastic optimization empirical risk minimization decision rule Reproducing Kernel Hilbert Spaces (RKHS) support vector machine (SVM) regularization convergence

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INFORMATICA

  • Online ISSN: 1822-8844
  • Print ISSN: 0868-4952
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