  Positive definite operator-valued kernels generalize the well-known notion of
reproducing kernels, and are naturally adapted to multi-output learning
situations. This paper addresses the problem of learning a finite linear
combination of infinite-dimensional operator-valued kernels which are suitable
for extending functional data analysis methods to nonlinear contexts. We study
this problem in the case of kernel ridge regression for functional responses
with an lr-norm constraint on the combination coefficients. The resulting
optimization problem is more involved than those of multiple scalar-valued
kernel learning since operator-valued kernels pose more technical and
theoretical issues. We propose a multiple operator-valued kernel learning
algorithm based on solving a system of linear operator equations by using a
block coordinatedescent procedure. We experimentally validate our approach on a
functional regression task in the context of finger movement prediction in
brain-computer interfaces.
