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Hierarchical estimation of parameters in Bayesian networks

Azzimonti, Laura, Corani, Giorgio, Zaffalon, Marco
Computational statistics & data analysis 2019 v.137 pp. 67-91
Bayesian theory, algorithms, case studies, models, probability
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.