Belief Propagation and Loop Series on Planar Graphs

@article{Chertkov2008BeliefPA,
  title={Belief Propagation and Loop Series on Planar Graphs},
  author={Michael Chertkov and Vladimir Y. Chernyak and Razvan Teodorescu},
  journal={CoRR},
  year={2008},
  volume={abs/0802.3950}
}
We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation [3], to evaluating the partition function of the dimer matching model on an auxiliary planar graph. Thus, the truncated series can be… CONTINUE READING

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