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Detection of an Arbitrary Number of Communities in a Block Spin Ising Model

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arxiv 2311.18112 v1 pith:IFGPEX4T submitted 2023-11-29 math.PR math.STstat.TH

Miguel Ballesteros , Ramsés H. Mena , José Luis Pérez , Gabor Toth This is my paper
classification math.PRmath.STstat.TH
keywords modelgroupsproblemspinblockcommunitiesdetectiondifferent
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We study the problem of community detection in a general version of the block spin Ising model featuring M groups, a model inspired by the Curie-Weiss model of ferromagnetism in statistical mechanics. We solve the general problem of identifying any number of groups with any possible coupling constants. Up to now, the problem was only solved for the specific situation with two groups of identical size and identical interactions. Our results can be applied to the most realistic situations, in which there are many groups of different sizes and different interactions. In addition, we give an explicit algorithm that permits the reconstruction of the structure of the model from a sample of observations based on the comparison of empirical correlations of the spin variables, thus unveiling easy applications of the model to real-world voting data and communities in biology.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Approximation Techniques for the Reconstruction of the Probability Measure and the Coupling Parameters in a Curie-Weiss Model for Large Populations

    math.ST 2025-07 conditional novelty 6.0 of 10

    A constant-cost, asymptotically normal estimator of Curie-Weiss interaction parameters is built from large-population moment approximations, with consistency in the double limit n, N to infinity.

  2. Reconstruction of the Probability Measure and the Coupling Parameters in a Curie-Weiss Model

    math.PR 2025-05 conditional novelty 6.0 of 10

    For the multi-group Curie-Weiss model, the maximum likelihood estimator of within-group coupling parameters is consistent, asymptotically normal, and exponentially concentrated, with an application to optimal voting weights.

  3. Reconstructing the Probability Measure of a Multi-group Curie-Weiss Model with Interacting Groups

    physics.soc-ph 2026-07 conditional novelty 4.0 of 10

    A margin-based moment estimator recovers the three coupling parameters of a two-group Curie-Weiss voting model with asymptotic normality in the weak-interaction regime; in the strong-interaction regime only the magnet...

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