PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Universal Multi-task Kernels
Charles A. Micchelli, Andrea Caponnetto, Massimiliano Pontil and Yiming Ying
Journal of Machine Learning Research Volume 9, 1615 - 1646, 2008. ISSN ISSN 1533-7928


In this paper we are concerned with reproducing kernel Hilbert spaces $\gmc{H}_K$ of functions from an input space into a Hilbert space ${\gmc{Y}},$ an environment appropriate for multi-task learning. The reproducing kernel $K$ associated to $\gmc{H}_K$ has its values as operators on $\gmc{Y}.$ 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 $\gmc{Y}$ 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.

PDF - Requires Adobe Acrobat Reader or other PDF viewer.
EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4253
Deposited By:Yiming Ying
Deposited On:29 December 2008