Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models

Daniel Levine, Jonathan How
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:648-656, 2014.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-levine14a, title = {Quantifying Nonlocal Informativeness in High-Dimensional, Loopy {G}aussian Graphical Models}, author = {Levine, Daniel and How, Jonathan}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {648--656}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/levine14a/levine14a.pdf}, url = {https://proceedings.mlr.press/r12/levine14a.html}, abstract = {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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models %A Daniel Levine %A Jonathan How %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-levine14a %I PMLR %P 648--656 %U https://proceedings.mlr.press/r12/levine14a.html %V R12 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Levine, D. & How, J.. (2014). Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:648-656 Available from https://proceedings.mlr.press/r12/levine14a.html. Reissued by PMLR on 04 October 2026.

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