Stable Causal Discovery via Directed Acyclic Graph Aggregation

2026-05-18

AI Summary

Learning a single directed acyclic graph (DAG) from data is often unstable due to model uncertainty, limited sample sizes, and an exponentially large search space. To address this, this work proposes DAGgr, a framework that aggregates candidate DAGs obtained across multiple data splits by weighting them according to their out-of-sample predictive likelihoods and then thresholding edge importance scores to produce a stable, strictly acyclic causal graph. DAGgr is the first method to achieve model averaging over DAGs while preserving acyclicity, for which it establishes finite-sample risk bounds and proves edge selection consistency under mild weighting conditions. Empirical results demonstrate that DAGgr matches or outperforms the best individual models in structure recovery across diverse simulated graphs and the Sachs protein signaling network, and substantially surpasses conventional bootstrap aggregation baselines.

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.

Problem

• causal discovery
• directed acyclic graph
• model uncertainty
• structural stability
• finite samples

Innovation

• causal discovery
• directed acyclic graph
• model averaging
• stability
• acyclicity