Consistent DAG selection for Bayesian Causal Discovery under general error distributions

Music City Center 

We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear acyclic structural equation model (SEM) with the associated errors being independent and allowed to be non-Gaussian. A Bayesian hierarchical model is proposed to identify the true data-generating directed acyclic graph (DAG) structure where the nodes and edges represent the variables and the direct causal effects, respectively. Moreover, incorporating the information of non-Gaussian errors, we characterize the distribution equivalence class of the true DAG, which specifies the best possible extent up to which the DAG can be identified based on purely observational data. Furthermore, under the consideration that the errors are distributed as some scale mixture of Gaussian, where the mixing distribution is unspecified, and mild distributional assumptions, we establish that the posterior probability of the distribution equivalence class of the true DAG converges to unity as the sample size grows. This shows that the proposed method achieves the posterior DAG selection consistency. Simulation studies are presented to illustrate the results, where we also demonstrate different rates of divergence of the associated posterior odds varying over the competing DAGs.

Causal discovery

Causal inference

Structural equation modeling

Bayesian model selection

Posterior consistency

Causal structure learning 

Section on Statistical Learning and Data Science