Jianqiang Liu, Charles A. Micchelli, Rui Wang, Yuesheng Xu
Abstract: Motivated by the importance of kernel-based methods for multi-task learning, we provide here a complete characterization of multi-task finite rank kernels in terms of the positivity of what we call its associated characteristic operator. Consequently, we are led to establishing that every continuous multi-task kernel, defined on a cube in an Euclidean space, not only can be uniformly approximated by multi-task polynomial kernels, but also can be extended as a multi-task kernel to all of the Euclidean space. Finally, we discuss the interpolation of multi-task kernels by multi-task finite rank kernels.
Journal: Adv. Comput. Math. 38 (2013), no. 2, 427–439
DOI: 10.1007/s10444-011-9244-x