A Gibbs sampler for learning DAG: a unification for discrete and Gaussian domains

References

• Pearl J. Probabilistic reasoning in intelligent systems: networks of plausible inference. San Mateo, CA: Morgan Kaufman; 1988.
   Google Scholar
• Cooper GF, Herskovits E. A Bayesian method for constructing Bayesian belief networks from databases. Uncertainty Proceedings 1991; Elsevier; 1991. p. 86–94.
   Google Scholar
• Spiegelhalter DJ, Dawid AP, Lauritzen SL, et al. Bayesian analysis in expert systems. Stat Sci. 1993;8(3):219–247.
   Web of Science ®Google Scholar
• Heckerman D, Geiger D, Chickering DM. Learning Bayesian networks: The combination of knowledge and statistical data. Proceedings of Tenth Conference on Uncertainty in Artificial Intelligence; 1994;20(3):293–301.
   Google Scholar
• Geiger D, Heckerman D. Learning gaussian networks. Proceedings of the Tenth international conference on Uncertainty in artificial intelligence; Morgan Kaufmann Publishers Inc; 1994. p. 235–243.
   Google Scholar
• Heckerman D, Geiger D. Learning Bayesian networks: a unification for discrete and Gaussian domains. Proceedings of the Eleventh conference on Uncertainty in artificial intelligenc; Morgan Kaufmann Publishers Inc; 1995. p. 274–284 .
   Google Scholar
• Friedman N, Koller D. Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning. 2003;50(1–2):95–125.
   Web of Science ®Google Scholar
• Giudici P, Castelo R. Improving Markov chain Monte Carlo model search for data mining. Machine Learning. 2003;50(1–2):127–158.
   Web of Science ®Google Scholar
• Madigan D, York J, Allard D. Bayesian graphical models for discrete data. Int Stat Rev/Revue Internationale de Statistique. 1995;63:215–232.
   Web of Science ®Google Scholar
• Niinimaki T, Parviainen P, Koivisto M. Partial order MCMC for structure discovery in Bayesian networks. 2012. Available from: arXiv:1202.3753.
   Google Scholar
• Rezaei Tabar V, Zareifard H, Salimi S, et al. An empirical bayes approach for learning directed acyclic graph using MCMC algorithm. Stat Anal Data Mining: The ASA Data Sci J. 2019;12(5):394–403.
   Web of Science ®Google Scholar
• Su C, Borsuk ME. Improving structure MCMC for Bayesian networks through Markov blanket resampling. J Machine Learning Res. 2016;17(1):4042–4061.
   Google Scholar
• Goudie RJ, Mukherjee S. A Gibbs sampler for learning DAGs. J Machine Learning Res. 2016;17(1):1032–1070.
   Google Scholar
• Rezaei Tabar V, Eskandari F, Salimi S, et al. Finding a set of candidate parents using dependency criterion for the K2 algorithm. Pattern Recogn Lett. 2018;111:23–29.
   Web of Science ®Google Scholar
• Cao X, Khar K, Ghosh M. Posterior graph selection and estimation consistency for high dimensional bayesian dag models. Ann Stat. 2019;47(1):319–348.
   Web of Science ®Google Scholar
• Aragam B, Amini A, Zhou Q. Learning directed acyclic graphs with penalized neighbourhood regression. 2015. Available from: https://arxiv.org/abs/1511.08963.
   Google Scholar
• Khare K, Oh S, Rahman S, et al. A convex framework for high-dimensional sparse cholesky based covariance estimation in gaussian dag models. Tech. Rep. 2017. Available from: https://arxiv.org/abs/1610.02436.
   Google Scholar
• Shojaie A, Michailidis G. Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika. 2010;97:519–538.
   PubMed Web of Science ®Google Scholar
• Geiger D, Heckerman D. Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Ann Statist. 2002;30:1412–1440.
   Web of Science ®Google Scholar
• Ben-David E, Li T, Massam H, et al. High dimensional Bayesian inference for Gaussian directed acyclic graph models. Tech. Rep. 2016. Available from: http://arxiv.org/abs/1109.4371.
   Google Scholar
• Wang H. Bayesian graphical lasso models and efficient posterior computation. Bayesian Anal. 2012;7(4):867–886.
   Web of Science ®Google Scholar
• Letac G, Massam H. Wishart distributions for decomposable graphs. Ann Stat. 2007;35:1278–1323.
   Web of Science ®Google Scholar
• Banerjee S, Ghosal S. Bayesian structure learning in graphical models. J Multivariate Anal. 2015;35:147–162.
   Web of Science ®Google Scholar
• Mitchell TJ, Beauchamp JJ. Bayesian variable selection in linear regression. J Amer Stat Assoc. 1988;83(404):1023–1032.
   Web of Science ®Google Scholar
• George EI, McCulloch RE. Approaches for Bayesian variable selection. Stat Sinica. 1997;7:339–373.
   Web of Science ®Google Scholar
• Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation. J Amer Stat Assoc. 1987;82(398):528–540.
   Web of Science ®Google Scholar
• Talhouk A, Doucet A, Murphy K. Efficient Bayesian inference for multivariate probit models with sparse inverse correlation matrices. J Comput Graphical Stat. 2012;21:739–757.
   Web of Science ®Google Scholar
• Guo J, Levina E, Michailidis G, et al. Graphical models for ordinal data. J Comput Graph Stat. 2015;24:183–204.
   PubMed Web of Science ®Google Scholar
• Mouchart M. A note on Bayes theorem. Statistica. 1976;36:25.
   Google Scholar
• Florens J-P, Mouchart M, Rolin J-M. Elements of Bayesian statistics. 1990.
   Google Scholar
• Albert J, Chib S. Bayesian analysis of binary and polychotomous response data. J Am Stat Assoc. 1993;88:669–679.
   Web of Science ®Google Scholar
• Bliss C. The calculation of the dosage-Mortality curve. Ann Appl Biol. 1935;22:134–167.
   Google Scholar
• Chib S, Greenberg E. Analysis of multivariate probit models. Biometrika. 1998;85:347–361.
   Web of Science ®Google Scholar
• Schäfer J, Strimmer K. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat Appl Genetics Mol Biol. 2005;4(1):32.
   Web of Science ®Google Scholar
• Scutari M, Howell P, Balding DJ, et al. Multiple quantitative trait analysis using Bayesian networks. Genetics. 2014;198(1):129–137.
   PubMed Web of Science ®Google Scholar
• Ripley BD. Pattern recognition via neural networks. Oxford Graduate Lectures on Neural Networks. Oxford University Press; 1996. [See Available from: http://www.stats.ox.ac.uk/ripley/papers.html].
   Google Scholar
• Khare K, Rajaratnam B. Wishart distributions for decomposable covariance graph models. Ann Stat. 2011;39:514–555.
   Web of Science ®Google Scholar