A Meta-Learning Approach to Bayesian Causal Discovery

TL;DR

This paper introduces a Bayesian meta-learning model that effectively samples from the causal structure posterior, capturing key properties and improving over existing methods in Bayesian causal discovery.

Contribution

It presents a novel meta-learning approach that encodes correlation and permutation invariance, enabling reliable sampling from the causal structure posterior.

Findings

Outperforms existing Bayesian causal discovery methods

Successfully samples from the causal structure posterior

Encodes key properties like correlation and permutation invariance

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 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.