A Generalized Representer Theorem

  • Bernhard Schölkopf
  • Ralf Herbrich
  • Alex J. Smola
Conference paper

DOI: 10.1007/3-540-44581-1_27

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2111)
Cite this paper as:
Schölkopf B., Herbrich R., Smola A.J. (2001) A Generalized Representer Theorem. In: Helmbold D., Williamson B. (eds) Computational Learning Theory. COLT 2001. Lecture Notes in Computer Science, vol 2111. Springer, Berlin, Heidelberg

Abstract

Wahba’s classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers and empirical risk terms, and give a self-contained proof utilizing the feature space associated with a kernel. The result shows that a wide range of problems have optimal solutions that live in the finite dimensional span of the training examples mapped into feature space, thus enabling us to carry out kernel algorithms independent of the (potentially infinite) dimensionality of the feature space.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Bernhard Schölkopf
    • 1
    • 2
    • 3
  • Ralf Herbrich
    • 1
    • 2
  • Alex J. Smola
    • 1
  1. 1.Department of EngineeringAustralian National UniversityCanberraAustralia
  2. 2.Microsoft Research Ltd.CambridgeUK
  3. 3.Biowulf TechnologiesNew YorkUSA

Personalised recommendations