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Maximum Entropy Relaxation for Graphical Model Selection Given Inconsistent Statistics

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3 Author(s)
Chandrasekaran, Venkat ; Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 ; Johnson, Jason K. ; Willsky, A.S.

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.

Published in:

Statistical Signal Processing, 2007. SSP '07. IEEE/SP 14th Workshop on

Date of Conference:

26-29 Aug. 2007