Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality
This work addresses high-dimensional regression and causal inference problems, offering a scalable method with theoretical guarantees, though it appears to be an incremental extension of existing kernel learning techniques.
The authors tackled high-dimensional nonlinear multivariate regression by proposing a matrix-valued multiple kernel learning framework with mixed norm regularizers, developing a scalable eigendecomposition-free algorithm that simultaneously learns input and output components of separable kernels, and applied it to extend Graphical Granger Causality techniques for causal inference.
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.