UCLA

Often casual Bayesian networks contain variables that we cannot observe or measure. If we wish to find an optimal graphical representation, typical structure learning cannot account for the existence of latent confounders. This results in possible bias and misleading results. Here we consider structure learning for a class of mixed graphs, bow-free acyclic mixed directed graphs, ADMGs, that offer a representation of directed acyclic graphs, DAGs, with latent confounders. Our approach uses a hybrid of constraint-based MAG learning and score-based optimization to find ADMGs with optimal BIC. We use constraint-based MAG learning to restrict our search space and then find the optimal ADMG representation using a score-based optimization algorithm. We also present a simulation and ADMG comparison framework that shows the empirical effectiveness of our alogrithm.