Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

Abstract

Abstract. This work presents two new score functions based on the Bayesian Dirichlet equivalent uniform (BDeu) score for learning Bayesian network structures. They consider the sensitivity of BDeu to varying parameters of the Dirichlet prior. The scores take on the most adversary and the most beneficial priors among those within a contamination set around the symmetric one. We build these scores in such way that they are decomposable and can be computed efficiently. Because of that, they can be integrated into any state-of-the-art structure learning method that explores the space of directed acyclic graphs and allows decomposable scores. Empirical results suggest that our scores outperform the standard BDeu score in terms of the likelihood of unseen data and in terms of edge discovery with respect to the true network, at least when the training sample size is small. We discuss the relation between these new scores and the accuracy of inferred models. Moreover, our new criteria can be used to identify the amount of data after which learning is saturated, that is, additional data are of little help to improve the resulting model.

Beyond Uniform Priors in Bayesian Network Structure Learning

“…The same is true for the optimal α proposed by Steck (2008) for BDeu, whose estimation requires multiple runs of the structure learning algorithm to converge. The Max-BDe and Min-BDe scores in Scanagatta et al (2014) overcome in part the limitations of BDeu by optimising for either goodness of fit at the expense of predictive accuracy, or vice versa. As a further term of comparison, we also included BIC in the simulation; while it outperforms U+BDeu in some circumstances and it is computationally efficient, MU+BDs is better overall in the DAGs it learns and competitive in predictive accuracy.…”

Averaged Extended Tree Augmented Naive Classifier

“…The experiment results we show herein were generated by learning our classifiers using 20 runs of 5-fold cross-validation, and so each classifier's learning procedure has been called 100 times per data set, and tested over the extra fold also 100 times. We use the Bayesian Dirichlet equivalent uniform (BDeu) score with hyper-parameter α * = 5 unless specified (it is not well understood how this affects the accuracy of classification and we will explore the results of a few different values α * as suggested in the literature [43][44][45], but a more detailed study on α * is beyond the scope of this work).…”

Integer Linear Programming for the Bayesian network structure learning problem

“…These scores have the property of local decomposability, meaning that the global score can be found as a simple function of the score associated with each node. In the current paper, we restrict ourselves to consideration of the BDeu score, though we note that the software presented has been used to learn networks based on other scores [8][9][10].…”