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

The purpose of this paper is to establish the notion of vector-valued reproducing kernel Banach spaces and demonstrate its applications to multi-task machine learning. Built on the theory of scalar-valued reproducing kernel Hilbert spaces (RKHS) [3], kernel methods have been proven successful in single task machine learning [10, 14, 29, 30, 33]. Multi-task learning where the unknown target function to be learned from finite sample data is vector-valued appears more often in practice. References [13, 25] proposed the development of kernel methods for learning multiple related tasks simultaneously. The mathematical foundation used there was the theory of vector-valued RKHS [5, 27].