Hybrid Copula Bayesian Networks

This paper introduces the hybrid copula Bayesian network (HCBN) model, a generalization of the copula Bayesian network (CBN) model developed by Elidan (2010) for continuous random variables to multivariate mixed probability distributions of discrete and continuous random variables. To this end, we extend the theorems proved by Nešlehová (2007) from bivariate to multivariate copulas with discrete and continuous marginal distributions. Using the multivariate copula with discrete and continuous marginal distributions as a theoretical basis, we construct an HCBN that can model all possible permutations of discrete and continuous random variables for parent and child nodes, unlike the popular conditional linear Gaussian network model. Finally, we demonstrate on a numerous synthetic datasets and a real life dataset that our HCBN compares favorably, from a modeling and flexibility viewpoint, to other hybrid models including the conditional linear Gaussian and the mixture of truncated exponentials models.