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
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
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
Y2 - 4 December 2006 through 7 December 2006
ER -