Belief propagation for networks with loops

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Article numbereabf1211
Journal / PublicationScience Advances
Volume7
Issue number17
Online published23 Apr 2021
Publication statusPublished - 23 Apr 2021
Externally publishedYes

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Abstract

Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here, we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving substantially on standard message passing methods. We also discuss potential applications of our method to a variety of other problems.

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Citation Format(s)

Belief propagation for networks with loops. / Kirkley, Alec; Cantwell, George T.; Newman, M. E. J.

In: Science Advances, Vol. 7, No. 17, eabf1211, 23.04.2021.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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