A Function Representation for Learning in Banach Spaces

  • Charles A. Micchelli
  • Massimiliano Pontil
Conference paper

DOI: 10.1007/978-3-540-27819-1_18

Volume 3120 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Micchelli C.A., Pontil M. (2004) A Function Representation for Learning in Banach Spaces. In: Shawe-Taylor J., Singer Y. (eds) Learning Theory. COLT 2004. Lecture Notes in Computer Science, vol 3120. Springer, Berlin, Heidelberg

Abstract

Kernel–based methods are powerful for high dimensional function representation. The theory of such methods rests upon their attractive mathematical properties whose setting is in Hilbert spaces of functions. It is natural to consider what the corresponding circumstances would be in Banach spaces. Led by this question we provide theoretical justifications to enhance kernel–based methods with function composition. We explore regularization in Banach spaces and show how this function representation naturally arises in that problem. Furthermore, we provide circumstances in which these representations are dense relative to the uniform norm and discuss how the parameters in such representations may be used to fit data.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Charles A. Micchelli
    • 1
  • Massimiliano Pontil
    • 2
  1. 1.Department of Mathematics and Statistics, State University of New YorkThe University at AlbanyAlbanyUSA
  2. 2.Department of Computer SciencesUniversity College LondonLondonEngland, UK