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Gaussian Directed Acyclic Graphs (DAGs) represent a powerful tool for learning the network of dependencies among variables, a task which is of primary interest in many fields and specifically in biology. Different DAGs may encode equivalent conditional independence structures, implying limited ability, with observational data, to identify causal relations. In many contexts however, measurements are collected under heterogeneous settings where variables are subject to exogenous interventions. Interventional data can improve the structure learning process whenever the targets of an intervention are known. However, these are often uncertain or completely unknown, as in the context of drug target discovery. We propose a Bayesian method for learning dependence structures and intervention targets from data subject to interventions on unknown variables of the system. Selected features of our approach include a DAG-Wishart prior on the DAG parameters, and the use of variable selection priors to express uncertainty on the targets. We provide theoretical results on the correct asymptotic identification of intervention targets and derive sufficient conditions for Bayes factor and posterior ratio consistency of the graph structure. Our method is applied in simulations and real-data world settings, to analyze perturbed protein data and assess antiepileptic drug therapies. Details of the MCMC algorithm and proofs of propositions are provided in the supplementary materials, together with more extensive results on simulations and applied studies. Supplementary materials for this article are available online. |
