Learning Bounds for Support Vector Machines with Learned Kernels

  • Nathan Srebro
  • Shai Ben-David
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4005)

Abstract

Consider the problem of learning a kernel for use in SVM classification. We bound the estimation error of a large margin classifier when the kernel, relative to which this margin is defined, is chosen from a family of kernels based on the training sample. For a kernel family with pseudodimensiondφ, we present a bound of \(\sqrt{\tilde{\mathcal{O}}{({d_{\phi}}+1/\gamma^2)}/n}\) on the estimation error for SVMs with margin γ. This is the first bound in which the relation between the margin term and the family-of-kernels term is additive rather then multiplicative. The pseudodimension of families of linear combinations of base kernels is the number of base kernels. Unlike in previous (multiplicative) bounds, there is no non-negativity requirement on the coefficients of the linear combinations. We also give simple bounds on the pseudodimension for families of Gaussian kernels.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nathan Srebro
    • 1
  • Shai Ben-David
    • 2
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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