Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models
Author(s)Levine, Daniel; How, Jonathan P.
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We consider the problem of selecting informative observations in Gaussian graphical models containing both cycles and nuisances. More specifically, we consider the subproblem of quantifying conditional mutual information measures that are nonlocal on such graphs. The ability to efficiently quantify the information content of observations is crucial for resource-constrained data acquisition (adaptive sampling) and data processing (active learning) systems. While closed-form expressions for Gaussian mutual information exist, standard linear algebraic techniques, with complexity cubic in the network size, are intractable for high-dimensional distributions. We investigate the use of embedded trees for computing nonlocal pairwise mutual information and demonstrate through numerical simulations that the presented approach achieves a significant reduction in computational cost over inversion-based methods.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Proceedings of the 2014 30th Conference on Uncertainty in Artifical Intelligence
Association of Uncertainty in Artifical Intelligence
Levine, Daniel, and Jonathan P. How. "Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models." 2014 30th Conference on Uncertainty in Artifical Intelligence, Quebec, Canada, July 23-27, 2014
Author's final manuscript