Kernels for Multi--task Learning

This paper provides a foundation for multi-task learning using reproducing kernel Hilbertspaces of vector-valued functions. In this setting, the kernel is a matrix-valued function. Some explicit examples will be described which go beyond ourearlier results in [7]. In particular, we characterize classes of matrix-valued kernels which are linear and are of the dot product or the translation invariant type.We discuss how these kernels can be used to model relations between the tasks and present linear multi-task learning algorithms. Finally, we present a novel proof of the representer theorem for a minimizer of a regularization functional whichis based on the notion of minimal norm interpolation.