A Meta-Learning Approach to Bayesian Causal Discovery
This work addresses the problem of uncertainty quantification in causal discovery for researchers and practitioners, representing an incremental improvement by extending meta-learning to full posterior estimation.
The paper tackles the challenge of approximating the Bayesian posterior over causal structures, which is difficult due to the large number of possible graphs and functional relationships. It proposes a Bayesian meta-learning model that enables sampling from the posterior and encodes key properties like edge correlation and permutation equivariance, showing advantages over existing methods.
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 meta-learning to view the problem of estimating the maximum a-posteriori causal graph as supervised learning. Yet, these methods are limited when estimating the full posterior as they fail to encode key properties of the posterior, such as correlation between edges and permutation equivariance with respect to nodes. Further, these methods also cannot reliably sample from the posterior over causal structures. 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.