Scalable Variational Causal Discovery Unconstrained by Acyclicity

TL;DR

This paper introduces a scalable Bayesian method for causal discovery that efficiently samples DAGs without explicit acyclicity constraints, enabling effective posterior inference over causal graphs.

Contribution

It proposes a novel differentiable DAG sampling technique that maps unconstrained distributions to valid DAGs, facilitating scalable variational Bayesian causal discovery.

Findings

Outperforms state-of-the-art baselines on simulated data

Demonstrates effectiveness on real datasets

Enables efficient posterior sampling of causal graphs

Abstract

Bayesian causal discovery offers the power to quantify epistemic uncertainties among a broad range of structurally diverse causal theories potentially explaining the data, represented in forms of directed acyclic graphs (DAGs). However, existing methods struggle with efficient DAG sampling due to the complex acyclicity constraint. In this study, we propose a scalable Bayesian approach to effectively learn the posterior distribution over causal graphs given observational data thanks to the ability to generate DAGs without explicitly enforcing acyclicity. Specifically, we introduce a novel differentiable DAG sampling method that can generate a valid acyclic causal graph by mapping an unconstrained distribution of implicit topological orders to a distribution over DAGs. Given this efficient DAG sampling scheme, we are able to model the posterior distribution over causal graphs using a simple variational distribution over a continuous domain, which can be learned via the variational inference framework. Extensive empirical experiments on both simulated and real datasets demonstrate the superior performance of the proposed model compared to several state-of-the-art baselines.