Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models
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...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Association of Uncertainty in Artifical Intelligence
2015
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| Online Access: | http://hdl.handle.net/1721.1/96957 https://orcid.org/0000-0001-8576-1930 |
| _version_ | 1826195998801657856 |
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| author | Levine, Daniel How, Jonathan P. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Levine, Daniel How, Jonathan P. |
| author_sort | Levine, Daniel |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:19:14Z |
| format | Article |
| id | mit-1721.1/96957 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:19:14Z |
| publishDate | 2015 |
| publisher | Association of Uncertainty in Artifical Intelligence |
| record_format | dspace |
| spelling | mit-1721.1/969572022-09-30T20:20:23Z Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models Levine, Daniel How, Jonathan P. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Levine, Daniel How, Jonathan P. 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. United States. Defense Advanced Research Projects Agency (Mathematics of Sensing, Exploitation and Execution) 2015-05-11T18:57:55Z 2015-05-11T18:57:55Z 2014-07 Article http://purl.org/eprint/type/ConferencePaper http://hdl.handle.net/1721.1/96957 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 https://orcid.org/0000-0001-8576-1930 en_US http://auai.org/uai2014/acceptedPapers.shtml Proceedings of the 2014 30th Conference on Uncertainty in Artifical Intelligence Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Association of Uncertainty in Artifical Intelligence MIT web domain |
| spellingShingle | Levine, Daniel How, Jonathan P. Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models |
| title | Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models |
| title_full | Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models |
| title_fullStr | Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models |
| title_full_unstemmed | Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models |
| title_short | Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models |
| title_sort | quantifying nonlocal informativeness in high dimensional loopy gaussian graphical models |
| url | http://hdl.handle.net/1721.1/96957 https://orcid.org/0000-0001-8576-1930 |
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