Belief propagation for permutations, rankings, and partial orders. (arXiv:2110.00513v2 [cs.AI] UPDATED)

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 the number of linear …

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