Maximum Entropy Relaxation for Graphical Model Selection Given Inconsistent Statistics

We develop a novel approach to approximate a specified collection of marginal distributions on subsets of variables by a globally consistent distribution on the entire collection of variables. In general, the specified marginal distributions may be inconsistent on overlapping subsets of variables. O...

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Bibliographic Details
Published in2007 IEEE/SP 14th Workshop on Statistical Signal Processing pp. 625 - 629
Main Authors Chandrasekaran, Venkat, Johnson, Jason K., Willsky, Alan S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.08.2007
Subjects
Biomedical signal processing
Entropy
Geophysics
Graphical models
inconsistent statistics
Laboratories
maximum entropy principle
model selection
Probability distribution
Random variables
Signal processing algorithms
Statistical distributions
Statistics
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Summary:We develop a novel approach to approximate a specified collection of marginal distributions on subsets of variables by a globally consistent distribution on the entire collection of variables. In general, the specified marginal distributions may be inconsistent on overlapping subsets of variables. Our method is based on maximizing entropy over an exponential family of graphical models, subject to divergence constraints on small subsets of variables that enforce closeness to the specified marginals. The resulting optimization problem is convex, and can be solved efficiently using a primal-dual interior-point algorithm. Moreover, this framework leads naturally to a solution that is a sparse graphical model.
ISBN:9781424411979
1424411971
ISSN:2373-0803
DOI:10.1109/SSP.2007.4301334