Monte Carlo methods for the ferromagnetic potts model using factor graph duality

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• dc.contributor.author Molkaraie, Mehdi
• dc.contributor.author Gómez, Vicenç
• dc.date.accessioned 2019-03-22T12:24:13Z
• dc.date.available 2019-03-22T12:24:13Z
• dc.date.issued 2018
• dc.description.abstract Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models. Specifically, we consider the problem of estimating the partition function of the ferromagnetic Ising and Potts models by Monte Carlo methods, which are known to work well at high temperatures but to fail at low temperatures. We propose Monte Carlo methods (uniform sampling and importance sampling) in the dual normal factor graph and demonstrate that they behave differently: they work particularly well at low temperatures. By comparing the relative error in estimating the partition function, we show that the proposed importance sampling algorithm significantly outperforms the state-of-the-art deterministic and Monte Carlo methods. For the ferromagnetic Ising model in an external field, we show the equivalence between the valid configurations in the dual normal factor graph and the terms that appear in the high-temperature series expansion of the partition function. Following this result, we discuss connections with Jerrum-Sinclair's polynomial randomized approximation scheme (the subgraphs-world process) for evaluating the partition function of ferromagnetic Ising models.
• dc.description.sponsorship This work was supported in part by the Spanish Ministry of Economy and Competitiveness through the Mara de Maeztu Units of Excellence Programme under Grant MDM-2015-0502 and in part by the Ramon y Cajal Program under Grant RYC-2015-18878 (AEI/MINEICO/FSE, UE).
• dc.format.mimetype application/pdf
• dc.identifier.citation Molkaraie M, Gómez V. Monte Carlo methods for the ferromagnetic potts model using factor graph duality. IEEE Trans Inf Theory. 2018 Jul 19;34(12):7449-64. DOI: 10.1109/TIT.2018.2857565
• dc.identifier.doi http://dx.doi.org/10.1109/TIT.2018.2857565
• dc.identifier.issn 0018-9448
• dc.identifier.uri http://hdl.handle.net/10230/36946
• dc.language.iso eng
• dc.publisher Institute of Electrical and Electronics Engineers (IEEE)
• dc.relation.ispartof IEEE Transactions on Information Theory. 2018 Jul 19;34(12):7449-64
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/RYC2015-18878
• dc.rights © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The final published article can be found at https://dx.doi.org/10.1109/TIT.2018.2857565
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Potts model
• dc.subject.keyword Ising model
• dc.subject.keyword Normal factor graph
• dc.subject.keyword Partition function
• dc.subject.keyword Dual normal factor graph
• dc.subject.keyword Monte Carlo methods
• dc.subject.keyword Low-temperature regime
• dc.subject.keyword Ferromagnetism
• dc.subject.keyword High-temperature series expansion
• dc.subject.keyword Subgraphs-world process
• dc.title Monte Carlo methods for the ferromagnetic potts model using factor graph duality
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion