Belief Propagation and Loop Series on Planar Graphs

@article{Chertkov2008BeliefPA,
  title={Belief Propagation and Loop Series on Planar Graphs},
  author={M. Chertkov and V. Chernyak and R. Teodorescu},
  journal={ArXiv},
  year={2008},
  volume={abs/0802.3950}
}
  • M. Chertkov, V. Chernyak, R. Teodorescu
  • Published 2008
  • Physics, Computer Science, Mathematics
  • ArXiv
  • We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R) [cond-mat/0601487]; 2006 J. Stat. Mech. P06009 [cond-mat/0603189]) 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 (Fisher 1961 Phys… CONTINUE READING
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