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19 April 2024 |
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Article overview
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Scalable Matrix-valued Kernel Learning and High-dimensional Nonlinear Causal Inference | | Vikas Sindhwani
; Aurelie C. Lozano
; Ha Quang Minh
; | | Date: |
17 Oct 2012 | | Abstract: | 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 (Michelli and Pontil, 2005). We develop a highly scalable and
eigendecomposition-free Block coordinate descent procedure that orchestrates
two inexact solvers: a Conjugate Gradient (CG) based Sylvester equation solver
for solving vector-valued Regularized Least Squares (RLS) problems, and a
specialized Sparse approximate SDP solver (Hazan, 2008) for learning output
kernels. As an application of our framework, we show how high-dimensional
causal inference tasks can be naturally cast as sparse function estimation
problems within our framework, leading to novel nonlinear extensions of Grouped
Graphical Granger Causality techniques. The algorithmic developments and
extensive empirical studies are complemented by theoretical analyses in terms
of Rademacher generalization bounds. | | Source: | arXiv, 1210.4792 | | Services: | Forum | Review | PDF | Favorites | |
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