Belief propagation for permutations, rankings, and partial orders

  title={Belief propagation for permutations, rankings, and partial orders},
  author={George T. Cantwell and Cristopher Moore},
  journal={Physical review. E},
  volume={105 5},
Many datasets give partial information about an ordering or ranking by indicating which team won a game, which item a user prefers, or who infected whom. We define a continuous spin system whose Gibbs distribution is the posterior distribution on permutations, given a probabilistic model of these interactions. Using the cavity method, we derive a belief propagation algorithm that computes the marginal distribution of each node's position. In addition, the Bethe free energy lets us approximate… 
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