Bayesian Optimal Experimental Design for Inferring Causal Structure

Inferring the causal structure of a system typically requires interven-tional data, rather than just observational data. Since interventional experiments can be costly, it is preferable to select interventions that yield the maximum amount of information about a system. We propose a novel Bayesian method for optimal experimental design by sequentially selecting interventions that minimize the expected posterior entropy as rapidly as possible. A key feature is that the method can be implemented by computing simple summaries of the current pos-terior, avoiding the computationally burdensome task of repeatedly performing posterior inference on hypothetical future datasets drawn from the posterior pre-dictive. After deriving the method in a general setting, we apply it to the problem of inferring causal networks. We present a series of simulation studies, in which we find that the proposed method performs favorably compared to existing alterna-tive methods. Finally, we apply the method to real data from two gene regulatory networks.