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Hierarchical estimation of parameters in Bayesian networks


  • Azzimonti, Laura
  • Corani, Giorgio
  • Zaffalon, Marco


A novel approach for parameter estimation in Bayesian networks is presented. The main idea is to introduce a hyper-prior in the Multinomial–Dirichletmodel, traditionally used for conditional distribution estimation in Bayesian networks. The resulting hierarchical model jointly estimates different conditional distributions belonging to the same conditional probability table, thus borrowing statistical strength from each other. An analytical study of the dependence structure a priori induced by the hierarchical model is performed and an ad hoc variational algorithm for fast and accurate inference is derived. The proposed hierarchical model yields a major performance improvement in classification with Bayesian networks compared to traditional models. The proposed variational algorithm reduces by two orders of magnitude the computational time, with the same accuracy in parameter estimation, compared to traditional MCMC methods. Moreover, motivated by a real case study, the hierarchical model is applied to the estimation of Bayesian networks parameters by borrowing strength from related domains.

Suggested Citation

  • Azzimonti, Laura & Corani, Giorgio & Zaffalon, Marco, 2019. "Hierarchical estimation of parameters in Bayesian networks," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 67-91.
  • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:67-91
    DOI: 10.1016/j.csda.2019.02.004

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    References listed on IDEAS

    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    3. Scutari, Marco, 2010. "Learning Bayesian Networks with the bnlearn R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i03).
    4. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    5. Grzegorczyk Marco & Husmeier Dirk, 2012. "A Non-Homogeneous Dynamic Bayesian Network with Sequentially Coupled Interaction Parameters for Applications in Systems and Synthetic Biology," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-62, July.
    6. Casella, George & Moreno, Elías, 2009. "Assessing Robustness of Intrinsic Tests of Independence in Two-Way Contingency Tables," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1261-1271.
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