Stable Causal Discovery via Directed Acyclic Graph Aggregation

TL;DR

DAGgr is a model averaging method for stable causal discovery that combines multiple DAGs based on predictive likelihood, ensuring acyclicity and improving structural accuracy.

Contribution

It introduces a novel aggregation framework for DAGs that guarantees acyclicity and enhances stability and accuracy over existing methods.

Findings

DAGgr matches or exceeds the best individual DAGs in simulations.

DAGgr outperforms bootstrap-aggregation baselines in structural recovery.

The method is validated on the Sachs et al. protein-signaling network.

Abstract

Directed Acyclic Graphs (DAGs) are central to uncovering causal structure in complex systems, yet learning a single DAG from data is often challenging: model uncertainty, finite samples, and a combinatorially large search space frequently yield unstable estimates. We propose DAGgr, a model averaging framework that aggregates multiple candidate DAGs into a single stable representation. Candidate graphs are weighted by their out-of-sample predictive likelihood across repeated data splits, and a thresholding rule on the resulting edge-importance scores guarantees that the aggregated graph is itself acyclic. We establish a finite-sample risk bound, prove that the procedure preserves acyclicity, and show that edge selection is consistent under mild conditions on the weights. Simulations across random, hub, and chain structures, together with an analysis of the Sachs et al. (2005) protein-signaling network, show that DAGgr matches or exceeds the best individual candidate while consistently outperforming bootstrap-aggregation baselines across structural recovery metrics.