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

Vikas Sindhwani, Ha Quang Minh, Aurelie Lozano
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:213-222, 2013.

Abstract

We propose a general matrix-valued mul- tiple kernel learning framework for high- dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, includ- ing those that induce sparsity, to be im- posed on a dictionary of vector-valued Repro- ducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition- free algorithm that orchestrates two inex- act solvers for simultaneously learning both the input and output components of separa- ble matrix-valued kernels. As a key appli- cation enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function esti- mation problems, leading to novel nonlinear extensions of a class of Graphical Granger Causality techniques. Our algorithmic de- velopments and extensive empirical studies are complemented by theoretical analyses in terms of Rademacher generalization bounds.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-sindhwani13a, title = {Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality}, author = {Sindhwani, Vikas and Minh, Ha Quang and Lozano, Aurelie}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {213--222}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/sindhwani13a/sindhwani13a.pdf}, url = {https://proceedings.mlr.press/r11/sindhwani13a.html}, abstract = {We propose a general matrix-valued mul- tiple kernel learning framework for high- dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, includ- ing those that induce sparsity, to be im- posed on a dictionary of vector-valued Repro- ducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition- free algorithm that orchestrates two inex- act solvers for simultaneously learning both the input and output components of separa- ble matrix-valued kernels. As a key appli- cation enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function esti- mation problems, leading to novel nonlinear extensions of a class of Graphical Granger Causality techniques. Our algorithmic de- velopments and extensive empirical studies are complemented by theoretical analyses in terms of Rademacher generalization bounds.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality %A Vikas Sindhwani %A Ha Quang Minh %A Aurelie Lozano %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-sindhwani13a %I PMLR %P 213--222 %U https://proceedings.mlr.press/r11/sindhwani13a.html %V R11 %X We propose a general matrix-valued mul- tiple kernel learning framework for high- dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, includ- ing those that induce sparsity, to be im- posed on a dictionary of vector-valued Repro- ducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition- free algorithm that orchestrates two inex- act solvers for simultaneously learning both the input and output components of separa- ble matrix-valued kernels. As a key appli- cation enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function esti- mation problems, leading to novel nonlinear extensions of a class of Graphical Granger Causality techniques. Our algorithmic de- velopments and extensive empirical studies are complemented by theoretical analyses in terms of Rademacher generalization bounds. %Z Reissued by PMLR on 04 October 2026.
APA
Sindhwani, V., Minh, H.Q. & Lozano, A.. (2013). Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:213-222 Available from https://proceedings.mlr.press/r11/sindhwani13a.html. Reissued by PMLR on 04 October 2026.

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