  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
autoregressive normalizing 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, ranging from causal discovery to making
interventional and counterfactual predictions. First, we show that causal
models derived from both affine and additive autoregressive flows with fixed
orderings over variables are identifiable, i.e. the true direction of causal
influence can be recovered. 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 can estimate normalized log-densities of data. Third, we
demonstrate that flows naturally allow for direct evaluation of both
interventional and counterfactual queries, the latter case being possible due
to the invertible nature of flows. 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.
