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Bayesian Methods

Statistically Valid Variational Bayes Algorithm for Ising Model Parameter Estimation

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Pages 75-84 | Received 05 May 2022, Accepted 10 May 2023, Published online: 30 Jun 2023

References

  • Anandkumar, A., Tan, V. Y., Huang, F., and Willsky, A. S. (2012), “High-Dimensional Structure Estimation in Ising Models: Local Separation Criterion,” The Annals of Statistics, 40, 1346–1375. DOI: 10.1214/12-AOS1009.
  • Baddeley, A. J. (1992), “An Error Metric for Binary Images,” Robust Computer Vision, 5978.
  • Basak, A., and Mukherjee, S. (2017), “Universality of the Mean-Field for the Potts Model,” Probability Theory and Related Fields, 168, 557–600. DOI: 10.1007/s00440-016-0718-0.
  • Bhattacharya, B. B., and Mukherjee, S. (2018), “Inference in Ising Models,” Bernoulli, 24, 493–525. DOI: 10.3150/16-BEJ886.
  • Boucheron, S., Lugosi, G., and Massart, P. (2013), Concentration Inequalities: A Nonasymptotic Theory of Independence, Oxford: Oxford University Press.
  • Bresler, G. (2015), “Efficiently Learning Ising Models on Arbitrary Graphs,” in Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing. DOI: 10.1145/2746539.2746631.
  • Brush, S. G. (1967), “History of the Lenz-Ising Model,” Reviews of Modern Physics, 39, 883. DOI: 10.1103/RevModPhys.39.883.
  • Chatterjee, S. (2007), “Estimation in Spin Glasses: A First Step,” The Annals of Statistics, 35, 1931–1946. DOI: 10.1214/009053607000000109.
  • Comets, F. (1992), “On Consistency of a Class of Estimators for Exponential Families of Markov Random Fields on the Lattice,” The Annals of Statistics, 20, 455–468. DOI: 10.1214/aos/1176348532.
  • Comets, F., and Gidas, B. (1991), “Asymptotics of Maximum Likelihood Estimators for the Curie-Weiss Model,” The Annals of Statistics, 19, 557–578. DOI: 10.1214/aos/1176348111.
  • Fang, Z., and Kim, I. (2016), “Bayesian Ising Graphical Model for Variable Selection,” Journal of Computational and Graphical Statistics, 25, 589–605. DOI: 10.1080/10618600.2015.1035438.
  • Ghosal, P., and Mukherjee, S. (2020), “Joint Estimation of Parameters in Ising Model,” The Annals of Statistics, 48, 785–810. DOI: 10.1214/19-AOS1822.
  • Gidas, B. (1988), “Consistency of Maximum Likelihood and Pseudo-likelihood Estimators for Gibbs Distributions,” in Stochastic Differential Systems, Stochastic Control Theory and Applications, eds. W. Fleming, and P.-L. Lions, pp. 129–145, New York: Springer.
  • Guyon, X., and Künsch, H. R. (1992), “Asymptotic Comparison of Estimators in the Ising Model,” in Stochastic Models, Statistical Methods, and Algorithms in Image Analysis, eds. P. Barone, A. Frigessi, M. Piccioni, pp. 177–198, New York: Springer.
  • Halim, S. (2007), “Modified Ising Model for Generating Binary Images,” Jurnal Informatika, 8, 115–118.
  • Haslbeck, J. M., Epskamp, S., Marsman, M., and Waldorp, L. J. (2021), “Interpreting the Ising Model: The Input Matters,” Multivariate Behavioral Research, 56, 303–313. DOI: 10.1080/00273171.2020.1730150.
  • Ising, E. (1924), “Beitrag zur theorie des ferro-und paramagnetismus,” Ph.D. thesis, Grefe & Tiedemann.
  • Lahtinen, V., and Pachos, J. (2017), “A Short Introduction to Topological Quantum Computation,” SciPost Physics, 3, 021. DOI: 10.21468/SciPostPhys.3.3.021.
  • Lee, K.-J., Jones, G. L., Caffo, B. S., and Bassett, S. S. (2014), “Spatial Bayesian Variable Selection Models on Functional Magnetic Resonance Imaging Time-Series Data,” Bayesian Analysis, 9, 699–732. DOI: 10.1214/14-BA873.
  • Leskovec, J., and Krevl, A. (2014), “SNAP Datasets: Stanford Large Network Dataset Collection,” available at http://snap.stanford.edu/data.
  • Li, F., and Zhang, N. R. (2010), “Bayesian Variable Selection in Structured High-Dimensional Covariate Spaces with Applications in Genomics,” Journal of the American Statistical Association, 105, 1202–1214. DOI: 10.1198/jasa.2010.tm08177.
  • Li, F., Zhang, T., Wang, Q., Gonzalez, M. Z., Maresh, E. L., and Coan, J. A. (2015), “Spatial Bayesian Variable Selection and Grouping for High-Dimensional Scalar-on-Image Regression,” The Annals of Applied Statistics, 9, 687–713. DOI: 10.1214/15-AOAS818.
  • Li, W., Huang, J., Li, X., Zhao, S., Lu, J., Han, Z. V., and Wang, H. (2021), “Recent Progresses in Two-Dimensional Ising Superconductivity,” Materials Today Physics, 21, 100504. DOI: 10.1016/j.mtphys.2021.100504.
  • Lipowski, A., Lipowska, D., and Ferreira, A. L. (2017), “Phase Transition and Power-Law Coarsening in an Ising-Doped Voter Model,” Physical Review E, 96, 032145. DOI: 10.1103/PhysRevE.96.032145.
  • Lokhov, A. Y., Vuffray, M., Misra, S., and Chertkov, M. (2018), “Optimal Structure and Parameter Learning of Ising Models,” Science Advances, 4, e1700791. DOI: 10.1126/sciadv.1700791.
  • Majewski, J., Li, H., and Ott, J. (2001), “The Ising Model in Physics and Statistical Genetics,” The American Journal of Human Genetics, 69, 853–862. DOI: 10.1086/323419.
  • Møller, J., Pettitt, A. N., Reeves, R., and Berthelsen, K. K. (2006), “An Efficient Markov Chain Monte Carlo Method for Distributions with Intractable Normalising Constants,” Biometrika, 93, 451–458. DOI: 10.1093/biomet/93.2.451.
  • Okabayashi, S., Johnson, L., and Geyer, C. J. (2011), “Extending Pseudo-Likelihood for Potts Models,” Statistica Sinica, 21, 331–347.
  • Park, J., Jin, I. H., and Schweinberger, M. (2022), “Bayesian Model Selection for High-Dimensional Ising Models, with Applications to Educational Data,” Computational Statistics & Data Analysis, 165, 107325. DOI: 10.1016/j.csda.2021.107325.
  • Ranganath, R., Gerrish, S., and Blei, D. (2014), “Black Box Variational Inference,” in Artificial Intelligence and Statistics, PMLR.
  • Ravikumar, P., Wainwright, M. J., and Lafferty, J. D. (2010), “High-Dimensional Ising Model Selection Using l1-regularized Logistic Regression,” The Annals of Statistics, 38, 1287–1319.
  • Robbins, H., and Monro, S. (1951), “A Stochastic Approximation Method,” The Annals of Mathematical Statistics, 22, 400–407. DOI: 10.1214/aoms/1177729586.
  • Smith, M., and Fahrmeir, L. (2007), “Spatial Bayesian Variable Selection with Application to Functional Magnetic Resonance Imaging,” Journal of the American Statistical Association, 102, 417–431. DOI: 10.1198/016214506000001031.
  • Xue, L., Zou, H., and Cai, T. (2012), “Nonconcave Penalized Composite Conditional Likelihood Estimation of Sparse Ising Models,” The Annals of Statistics, 40, 1403–1429. DOI: 10.1214/12-AOS1017.
  • Yang, Y., Pati, D., and Bhattacharya, A. (2020), “α-variational Inference with Statistical Guarantees,” Annals of Statistics, 48, 886–905.
  • Zhang, F., and Gao, C. (2020), “Convergence Rates of Variational Posterior Distributions,” Annals of Statistics, 48, 2180–2207.

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