A Meta-Learning Approach to Bayesian Causal Discovery

Abstract

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often necessary for downstream tasks. Finding an accurate approximation to this posterior is challenging, due to the large number of possible causal graphs, as well as the difficulty in the subproblem of finding posteriors over the functional relationships of the causal edges. Recent works have used Bayesian meta learning to view the problem of posterior estimation as a supervised learning task. Yet, these methods are limited as they cannot reliably sample from the posterior over causal structures and fail to encode key properties of the posterior, such as correlation between edges and permutation equivariance with respect to nodes. To address these limitations, we propose a Bayesian meta learning model that allows for sampling causal structures from the posterior and encodes these key properties. We compare our meta-Bayesian causal discovery against existing Bayesian causal discovery methods, demonstrating the advantages of directly learning a posterior over causal structure.