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A function representation for learning in Banach spaces

Micchelli, CA; Pontil, M; (2004) A function representation for learning in Banach spaces. In: ShaweTaylor, J and Singer, Y, (eds.) LEARNING THEORY, PROCEEDINGS. (pp. 255 - 269). SPRINGER-VERLAG BERLIN

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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 axe dense relative to the uniform norm and discuss how the parameters in such representations may be used to fit data.

Type: Proceedings paper
Title: A function representation for learning in Banach spaces
Event: 17th Annual Conference on Learning Theory (COLT 2004)
Location: Banff, CANADA
Dates: 2004-07-01 - 2004-07-04
ISBN: 3-540-22282-0
UCL classification: UCL > School of BEAMS > Faculty of Engineering Science
UCL > School of BEAMS > Faculty of Engineering Science > Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/158377
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