Structural learning and estimation of joint causal effects among network-dependent variables

Bayesian networks in the form of Directed Acyclic Graphs (DAGs) represent an effective tool for modeling and inferring dependence relations among variables, a process known as structural learning. In addition, when equipped with the notion of intervention, a causal DAG model can be adopted to quantify the causal effect on a response due to a hypothetical intervention on some variable. Observational data cannot distinguish between DAGs encoding the same set of conditional independencies (Markov equivalent DAGs), which however can be different from a causal perspective. In addition, because causal effects depend on the underlying network structure, uncertainty around the DAG generating model crucially affects the causal estimation results. We propose a Bayesian methodology which combines structural learning of Gaussian DAG models and inference of causal effects as arising from simultaneous interventions on any given set of variables in the system. Our approach fully accounts for the uncertainty around both the network structure and causal relationships through a joint posterior distribution over DAGs, DAG parameters and then causal effects.