Approximate inference using planar graph decomposition

Amir Globerson*, Tommi Jaakkola

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. The resulting algorithm also allows for the estimation of marginals. We compare our planar decomposition to the tree decomposition method of Wainwright et. al., showing that it results in a much tighter bound on the partition function, improved pairwise marginals, and comparable singleton marginals.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
Number of pages8
StatePublished - 2007
Externally publishedYes
Event20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada
Duration: 4 Dec 20067 Dec 2006

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference20th Annual Conference on Neural Information Processing Systems, NIPS 2006
CityVancouver, BC


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