A New Bayesian Approach to Learning Hybrid Bayesian Networks

Marco Grzegorczyk, Groningen University, NL

Abstract: We propose a new approach for learning the structure of Bayesian networks from hybrid data, that is, data containing both continuous (Gaussian) and discrete (categorical) variables. Consistent with state-of-the-art hybrid Bayesian network models, we do not allow discrete variables to have continuous parent nodes. Our model differs from existing approaches by incorporating discrete variables through multivariate linear regression rather than mixture modeling. Specifically, we apply multivariate linear regression, using the discrete variables as potential covariates, to adjust the means of the continuous Gaussian variables while simultaneously learning the dependencies among them. For each continuous variable, we infer a separate regression model with its own set of covariates (discrete parent nodes).