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 Bayesian network is how to model networks which 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 which is designed for a mixture of discrete and continuous variables, or continuous random variables are discretized, resulting in discrete Bayesian networks. In this paper, we propose a strategy to model all random variables as Gaussian, referred to it as {\it Run it As Gaussian (RAG)}. We demonstrate that RAG results in more reliable estimates of graph structures theoretically and by simulation studies, than converting continuous random variables to discrete. 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 strategy is more reliable.
翻译:Bayesian 网络被用作一种机制,以灵活和可解释的方式代表多个随机变量的联合分布。学习Bayesian网络结构的一个主要挑战是如何模拟包含连续和离散随机变量(称为Bayesian混合网络)的网络。本文概述了关于处理Bayesian混合网络的方法的文献。通常采取两种方法之一:要么认为数据具有联合分布,为离散和连续变量的混合设计,要么认为连续随机变量是分散的,从而形成离散的Bayesian 网络。在本文件中,我们提出了一个战略,将所有随机变量都作为Gaussian 模型,称为 {it Ruring it As Gausian (RAG)}。我们证明RAG在理论上和模拟研究中得出了更可靠的图表结构估算结果,而不是将连续随机变量转换为离散。两种战略也是在儿童肥胖数据集中执行的。两种不同的战略在最佳图形结构中产生了显著的差异,模拟研究的结果表明我们的战略更加可靠。