Vector-valued reproducing kernel Banach spaces with applications to multi-task learning

Authors:
Haizhang Zhang;Jun Zhang
Affiliations:
School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzho ...;Department of Psychology, University of Michigan, Ann Arbor, MI 48109, USA
Venue:
Journal of Complexity
Year:
2013

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Abstract

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBSs). 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 RKBSs. 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 RKBSs are established.