Variational Causal Networks: Approximate Bayesian Inference over Causal Structures
This addresses the problem of quantifying uncertainty in causal inference for robust decision-making, representing an incremental advance in scalable Bayesian methods.
The paper tackles the intractability of Bayesian inference over causal structures by proposing variational causal networks, an autoregressive variational family for approximating the posterior over directed acyclic graphs, and demonstrates in experiments that it provides a good approximation of the true posterior.
Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov equivalence class thereof. However, a crucial aspect to acting intelligently upon the knowledge about causal structure which has been inferred from finite data demands reasoning about its uncertainty. For instance, planning interventions to find out more about the causal mechanisms that govern our data requires quantifying epistemic uncertainty over DAGs. While Bayesian causal inference allows to do so, the posterior over DAGs becomes intractable even for a small number of variables. Aiming to overcome this issue, we propose a form of variational inference over the graphs of Structural Causal Models (SCMs). To this end, we introduce a parametric variational family modelled by an autoregressive distribution over the space of discrete DAGs. Its number of parameters does not grow exponentially with the number of variables and can be tractably learned by maximising an Evidence Lower Bound (ELBO). In our experiments, we demonstrate that the proposed variational posterior is able to provide a good approximation of the true posterior.