Causal Discovery from Databases with Discrete and Continuous Variables

Abstract

Bayesian Constraint-based Causal Discovery (BCCD) is a state-of-the-art method for robust causal discovery in the presence of latent variables. It combines probabilistic estimation of Bayesian networks over subsets of variables with a causal logic to infer causal statements. Currently BCCD is limited to discrete or Gaussian variables. Most of the real-world data, however, contain a mixture of discrete and continuous variables. We here extend BCCD to be able to handle combinations of discrete and continuous variables, under the assumption that the relations between the variables are monotonic. To this end, we propose a novel method for the efficient computation of BIC scores for hybrid Bayesian networks. We demonstrate the accuracy and efficiency of our approach for causal discovery on simulated data as well as on real-world data from the ADHD-200 competition.