Support vector machines are universally consistent

  • Authors:
  • Ingo Steinwart

  • Affiliations:
  • Mathematisches Institut, Friedrich-Schiller-Universität, 07743 Jena, Germany

  • Venue:
  • Journal of Complexity
  • Year:
  • 2002

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Abstract

We show that support vector machines of the 1-norm soft margin type are universally consistent provided that the regularization parameter is chosen in a distinct manner and the kernel belongs to a specific class-the so-called universal kernels-which has recently been considered by the author. In particular it is shown that the 1-norm soft margin classifier with Gaussian RBF kernel on a compact subset X of Rd and regularization parameter cn = nβ-1 is universally consistent, if n is the training set size and 0 β 1/d.