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 con- taining both cycles and nuisances. More specif- ically, we consider the subproblem of quantify- ing conditional mutual information measures that are nonlocal on such graphs. The ability to effi- ciently quantify the information content of obser- vations is crucial for resource-constrained data acquisition (adaptive sampling) and data process- ing (active learning) systems. While closed- form expressions for Gaussian mutual informa- tion exist, standard linear algebraic techniques, with complexity cubic in the network size, are in- tractable for high-dimensional distributions. We investigate the use of embedded trees for com- puting nonlocal pairwise mutual information and demonstrate through numerical simulations that the presented approach achieves a significant re- duction 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 con- taining both cycles and nuisances. More specif- ically, we consider the subproblem of quantify- ing conditional mutual information measures that are nonlocal on such graphs. The ability to effi- ciently quantify the information content of obser- vations is crucial for resource-constrained data acquisition (adaptive sampling) and data process- ing (active learning) systems. While closed- form expressions for Gaussian mutual informa- tion exist, standard linear algebraic techniques, with complexity cubic in the network size, are in- tractable for high-dimensional distributions. We investigate the use of embedded trees for com- puting nonlocal pairwise mutual information and demonstrate through numerical simulations that the presented approach achieves a significant re- duction 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 con- taining both cycles and nuisances. More specif- ically, we consider the subproblem of quantify- ing conditional mutual information measures that are nonlocal on such graphs. The ability to effi- ciently quantify the information content of obser- vations is crucial for resource-constrained data acquisition (adaptive sampling) and data process- ing (active learning) systems. While closed- form expressions for Gaussian mutual informa- tion exist, standard linear algebraic techniques, with complexity cubic in the network size, are in- tractable for high-dimensional distributions. We investigate the use of embedded trees for com- puting nonlocal pairwise mutual information and demonstrate through numerical simulations that the presented approach achieves a significant re- duction 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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