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We propose a general matrix-valued multiple kernel learning framework forhigh-dimensional nonlinear multivariate regression problems. This frameworkallows a broad class of mixed norm regularizers, including those that inducesparsity, to be imposed on a dictionary of vector-valued Reproducing KernelHilbert Spaces. We develop a highly scalable and eigendecomposition-freealgorithm that orchestrates two inexact solvers for simultaneously learningboth the input and output components of separable matrix-valued kernels. As akey application enabled by our framework, we show how high-dimensional causalinference tasks can be naturally cast as sparse function estimation problems,leading to novel nonlinear extensions of a class of Graphical Granger Causalitytechniques. Our algorithmic developments and extensive empirical studies arecomplemented by theoretical analyses in terms of Rademacher generalizationbounds.

Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality