Continuity approximation in hybrid Bayesian networks structure learning

Bayesian networks have been used to represent the joint distribution of multiple random variables in a flexible yet interpretable manner. One major challenge in learning the structure of a Bayesian network is how to model networks that include a mixture of continuous and discrete random variables, known as hybrid Bayesian networks. This paper overviews the literature on approaches to handle hybrid Bayesian networks. Typically, one of two approaches is taken: either the data are considered to have a joint distribution, designed for a mixture of discrete and continuous variables, or continuous random variables are discretized, resulting in discrete Bayesian networks. This paper proposes a strategy to model all random variables as Gaussian, referred to as Run it As Gaussian ( RAG ). We demonstrate that RAG results in more reliable estimates of graph structures theoretically and by simulation studies than other strategies. Both strategies are also implemented on a childhood obesity data set. The two different strategies give rise to significant differences in the optimal graph structures, with the results of the simulation study suggesting that our approach is more reliable.