Stability of Multi-Task Kernel Regression Algorithms

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 problems with nonscalar outputs like multi-task learning and structured output 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 generalization 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.