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

By Vikas Sindhwani, Ha Quang Minh, Aurelie C. Lozano. 2012

63 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Mechanics, Statistics and Probability

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Citations in the corpus

Operator-valued Kernels for Learning from Functional Response Data (2015, background): “Recent works in this direction includes the papers of Dinuzzo et al. (2011), Kadri et al. (2012), Sindhwani et al. (2013) and Lim et al. (2015), but further investigations are needed in this area.”
Multi-Task Multiple Kernel Relationship Learning (2016, methodology): “greturns from 9 companies as shown in table 1. The dataset is split evenly such that the ﬁrst 26 weeks of the year is used as the training set and the next 26 weeks is used as the test set. Following [21], we use univariate Gaussian kernels with 13 varying bandwidth, generated from each feature, as ”
Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators (2013, methodology): “Following [13, 18], our independence test can further be combined to recent developments in kernel time series prediction techniques [20] to define general and reliable multivariate causal inference techniques.”
Neural Granger Causality (2021, background): “The latter is the most mature of a sequence of nonlinear kernel Granger causality detection methods [60], [61].”