Vector-valued Reproducing Kernel Banach Spaces with Applications to   Multi-task Learning
  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. 
Haizhang Zhang, Jun Zhang
math.FA stat.ML