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A structural equation model (SEM) is an effective framework to reason overcausal relationships represented via a directed acyclic graph (DAG). Recentadvances have enabled effective maximum-likelihood point estimation of DAGsfrom observational data. However, a point estimate may not accurately capturethe uncertainty in inferring the underlying graph in practical scenarios,wherein the true DAG is non-identifiable and/or the observed dataset islimited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variationalinference framework for estimating a distribution over DAGs characterizing alinear-Gaussian SEM. Developing a full Bayesian posterior over DAGs ischallenging due to the the discrete and combinatorial nature of graphs. Weanalyse key design choices for scalable VI over DAGs, such as 1) theparametrization of DAGs via an expressive variational family, 2) a continuousrelaxation that enables low-variance stochastic optimization, and 3) suitablepriors over the latent variables. We provide a series of experiments on realand synthetic data showing that BCD Nets outperform maximum-likelihood methodson standard causal discovery metrics such as structural Hamming distance in lowdata regimes.

BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery