ENHANCING BAYESIAN NETWORKS THROUGH LOGISTIC REGRESSION: A CASE STUDY OF CZECH SOCIETY DIVISIONS

Abstract

One of the most frequently employed criteria for the structural learning of Bayesian networks (BNs) is the Bayesian Information Criterion (BIC). The objective is to identify a model that exhibits an optimal balance between the fit to the training data, as measured by the log-likelihood, and the model's complexity, as quantified by the number of model parameters. A significant challenge associated with this approach pertains to the exponential increase in the number of parameters required for conditional probability tables (CPTs) as the number of parents of each node increases. This phenomenon leads to a substantial growth in the complexity of the CPTs, which serve as the fundamental building blocks of BNs. However, there exist models of CPTs whose number of parameters grows linearly with the number of parents, and they often represent a better fit to data than general CPTs. In this paper, we examine models with CPTs, either in their general form or in the form corresponding to multinomial logistic regression (MLR) or ordinal logistic regression (OLR). We employ data from a sociological study entitled "Dividing Lines in Czech Society" to demonstrate the enhancement through the incorporation of MLR and OLR models as CPTs within the framework of BN structural learning.