VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries

Graph Neural Networks (GNNs) are a powerful tool for graph representation learning and have been proven to excel in practical complex problems like neural machine translation [1], traffic forecasting [5, 47], or drug discovery [11]. In this work, we investigate to which extent the inductive bias of GNNs-encoding the causal graph information-can be exploited to answer interventional and counterfactual queries. More specifically, to approximate the interventional and counterfactual distributions induced by interventions on a casual model. To this end, we assume i) causal sufficiency-i.e., absence of hidden confounders; and, ii) access to observational data and the true causal graph. We stress that the causal graph can often be inferred from expert knowledge [52] or via one of the approaches for causal discovery [12, 42]. With this analysis we aim to complement the concurrent line of research that theoretically studies the use of Neural Networks (NN) [45], and more recently GNNs [49], for causal inference. To this end, we describe the architectural design conditions that a variational graph autoencoder (VGAE)-as a density estimator that leverages a priori graph structure-must fulfill so that it can approximate causal interventions (do-operator) and abduction-action-prediction steps [33]. The resulting Variational Causal Graph Autoencoder, referred to as VACA, enables approximating the observational, interventional and counterfactual distributions induced by a causal model with unknown structural equations. We remark that parametric assumptions on the structural causal equations are in general not testable, may thus not hold in practice [34] and may lead to inaccurate results, if misspecified.