TY - GEN

T1 - Approximate inference using planar graph decomposition

AU - Globerson, Amir

AU - Jaakkola, Tommi

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77951944523&partnerID=8YFLogxK

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AN - SCOPUS:77951944523

SN - 9780262195683

T3 - Advances in Neural Information Processing Systems

SP - 473

EP - 480

BT - Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference

T2 - 20th Annual Conference on Neural Information Processing Systems, NIPS 2006

Y2 - 4 December 2006 through 7 December 2006

ER -