Belief propagation for permutations, rankings, and partial orders

George T. Cantwell; Cristopher Moore

doi:10.1103/physreve.105.l052303

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arXiv · 2110.00513

Belief propagation for permutations, rankings, and partial orders

George T. Cantwell·Cristopher Moore

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Abstract

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 extensions of a partial order and perform model selection between competing probabilistic models, such as the Bradley-Terry-Luce model of noisy comparisons and its cousins.

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cs.AI cond-mat.stat-mech cs.LG cs.SI stat.ML

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George T. Cantwell, Cristopher Moore. 2021-10-01. Belief propagation for permutations, rankings, and partial orders. https://doi.org/10.1103/physreve.105.l052303

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