Causal Discovery with a Mixture of DAGs

Abstract

Real causal processes may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs (DAGs); each sample follows a joint distribution that factorizes according to a DAG, but the DAG may differ between samples due to multiple independent factors. We then introduce an algorithm called Causal Inference over Mixtures that uses longitudinal data to infer a graph summarizing the causal relations generated from a mixture of DAGs even when cycles, non-stationarity, latent variables or selection bias exist. Experiments demonstrate improved performance in inferring ancestral relations as compared to prior approaches. R code is available at https://github.com/ericstrobl/CIM.