Statistically Valid Variational Bayes Algorithm for Ising Model Parameter Estimation

Minwoo Kim, Shrijita Bhattacharya, Tapabrata Maiti

Research output: Contribution to journalArticlepeer-review


Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant in the likelihood. Here, we use a pseudo-likelihood instead, to study the Bayesian estimation of two-parameter, inverse temperature and magnetization, Ising model with a fully specified coupling matrix. We develop a computationally efficient variational Bayes procedure for model estimation. Under the Gaussian mean-field variational family, we derive posterior contraction rates of the variational posterior obtained under the pseudo-likelihood. We also discuss the loss incurred due to variational posterior over true posterior for the pseudo-likelihood approach. Extensive simulation studies validate the efficacy of mean-field Gaussian and bivariate Gaussian families as the possible choices of the variational family for inference of Ising model parameters. Supplementary materials for this article are available online.
Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
StatePublished - Jun 30 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-07-17
Acknowledgements: The authors are grateful to P. Ghosal and S. Mukherjee for kindly sharing codes of their work. The research is partially supported by the National Science Foundation grants NSF DMS-1952856 and 1924724. We are thankful to the Associate Editor and the Reviewers for their comments which helped improve the manuscript significantly.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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