Structure Learning for Hybrid Bayesian Networks

Bayesian networks have been used as a mechanism to represent the joint distribution of multiple random variables in a flexible yet interpretable manner. One major challenge in learning the structure of a network is how to model networks which include a mixture of continuous and discrete random variables, known as hybrid Bayesian networks. This paper reviews the literature on approaches to handle hybrid Bayesian networks. When working with hybrid Bayesian networks, typically one of two approaches is taken: either the data are considered to have a joint multivariate Gaussian distribution, irrespective of the true distribution, or continuous random variables are discretized, resulting in discrete Bayesian networks. In this paper, we show that a strategy to model all random variables as Gaussian outperforms the strategy which converts the continuous random variables to discrete. We demonstrate the superior performance of our strategy over the latter, theoretically and by simulation studies for various settings. 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 the inference from the strategy assuming all random variables are Gaussian is more reliable.