PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Universal multi-task kernels
Andreas Caponnetto, Charles Micchelli, Massimiliano Pontil and Yiming Ying
(2007) Technical Report. UCL.


In this paper we are concerned with reproducing kernel Hilbert spaces HK of functions from an input space into a Hilbert space Y, an environment appropriate for multi-task learning. The reproducing kernel K associated to HK has its values as operators on Y. Our primary goal here is to derive conditions which ensure that the kernel K is universal. This means that on every compact subset of the input space, every continuous function with values in Y can be uniformly approximated by sections of the kernel. We provide various characterizations of universal kernels and highlight them with several concrete examples of some practical importance. Our analysis uses basic principles of functional analysis and especially the useful notion of vector measures which we describe in sufficient detail to clarify our results.

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EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3780
Deposited By:Massimiliano Pontil
Deposited On:22 February 2008