Causal Autoregressive Flows

Two apparently unrelated fields -- normalizing flows and causality -- have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of flows and identifiable causal models. We exploit the fact that autoregressive flow architectures define an ordering over variables, analogous to a causal ordering, to show that they are well-suited to performing a range of causal inference tasks. First, we show that causal models derived from both affine and additive flows are identifiable. This provides a generalization of the additive noise model well-known in causal discovery. Second, we derive a bivariate measure of causal direction based on likelihood ratios, leveraging the fact that flow models estimate normalized log-densities of data. Such likelihood ratios have well-known optimality properties in finite-sample inference. Third, we demonstrate that the invertibility of flows naturally allows for direct evaluation of both interventional and counterfactual queries. Finally, throughout a series of experiments on synthetic and real data, the proposed method is shown to outperform current approaches for causal discovery as well as making accurate interventional and counterfactual predictions.