Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms

Abstract: Aiming at a mathematical foundation for kernel methods in coefficient regularization for multi-task learning, we investigate theory of vector-valued reproducing kernel Banach spaces (RKBS) with L_{p,1}-norms, which contains the sparse learning scheme $p=1$ and the group lasso p=2. We construct RKBSs that are equipped with such group lasso norms and admit the linear representer theorem for regularized learning schemes. The corresponding kernels that are admissible for the construction are discussed.