  We study the stability properties of nonlinear multi-task regression in
reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a.
multi-task kernels, are appropriate for learning prob- lems with nonscalar
outputs like multi-task learning and structured out- put prediction. We show
that multi-task kernel regression algorithms are uniformly stable in the
general case of infinite-dimensional output spaces. We then derive under mild
assumption on the kernel generaliza- tion bounds of such algorithms, and we
show their consistency even with non Hilbert-Schmidt operator-valued kernels .
We demonstrate how to apply the results to various multi-task kernel regression
methods such as vector-valued SVR and functional ridge regression.
