Vector-valued Reproducing Kernel Banach Spaces with Applications to Multi-task Learning

TL;DR

This paper introduces vector-valued reproducing kernel Banach spaces (RKBS) for multi-task learning, exploring their properties, constructions, and applications, including a representer theorem for regularized learning schemes.

Contribution

It develops the theory of vector-valued RKBS, including properties, examples, and a new representer theorem for multi-task learning in Banach spaces.

Findings

Established basic properties and examples of vector-valued RKBS

Developed a representer theorem for regularized learning in these spaces

Applied the theory to multi-task machine learning problems

Abstract

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RKBS. The theory is then applied to multi-task machine learning. Especially, the representer theorem and characterization equations for the minimizer of regularized learning schemes in vector-valued RKBS are established.