Towards Scalable Bayesian Learning of Causal DAGs

Abstract

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks, which enables efficient approximate sampling from the graph posterior, provided that each node is assigned a small number K of candidate parents. We present algorithmic tricks to significantly reduce the space and time requirements of the method, making it feasible to use substantially larger values of K. Furthermore, we investigate the problem of selecting the candidate parents per node so as to maximize the covered posterior mass. Finally, we combine our sampling method with a novel Bayesian approach for estimating causal effects in linear Gaussian DAG models. Numerical experiments demonstrate the performance of our methods in detecting ancestor-descendant relations, and in effect estimation our Bayesian method is shown to outperform existing approaches.Preprint. Under review.

Inference for a Large Directed Graphical Model with Interventions

“…In a directed acyclic graph (DAG) model, the research has been centered on the reconstruction of directed relations in observational and interventional studies (Heinze-Deml et al, 2018;Zheng et al, 2018;Chickering, 2003;van de Geer and Bühlmann, 2013;Yuan et al, 2019;Oates et al, 2016;Aragam et al, 2019;Zhou et al, 2021). For inference, Bayesian methods (Friedman and Koller, 2003;Luo and Zhao, 2011;Viinikka et al, 2020) have been popular. Yet, statistical inference remains under-studied, especially for intervention models in high dimensions (Peters et al, 2016;Rothenhäusler et al, 2019).…”