Universal Multi-Task Kernels

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. Keywords. Multi-task learning, multi-task kernels, universal approximation, vector-valued reproducing kernel Hilbert spaces. c XXXX Andrea Caponnetto, Charles A. Micchelli, Massim...

• Type: Journal
• Year: 2008
• Where: JMLR
• Authors: Andrea Caponnetto, Charles A. Micchelli, Massimiliano Pontil, Yiming Ying
• Keywords: Input Space, JMLR 2008, Kernel Hilbert, Reproducing Kernel