Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality
Vikas Sindhwani, Ha Quang Minh, Aurelie Lozano
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function estimation problems, leading to novel nonlinear extensions of a class of Graphical Granger Causality techniques. Our algorithmic developments and extensive empirical studies are complemented by theoretical analyses in terms of Rademacher generalization bounds.
PDF Link: /papers/13/p586-sindhwani.pdf
AUTHOR = "Vikas Sindhwani
and Ha Quang Minh and Aurelie Lozano",
TITLE = "Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "586--595"