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Approximate Inference on Planar Graphs using Loop Calculus and Belief Propagation

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Figure

Figure 1: Example. (a) A Forney graph. (b) Corresponding extended graph. (c) Loops (in bold)included in the 2-regular partition function
Figure 2: Fisher’s rules. (Top) A node a of degree two in G is split in two nodes in Gext
Figure 3: Planar bipartite factor graph used to compare the full Pfaffian series with the loop series.Circles and black squares denote variables and factors respectively.
Figure 4 shows the error Ztions. For weak interactions ( (first column) and Z (second column) for both representa-β = 0.1) BP converges fast and provides an accurate approximation
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