Score-Based Learning of Cluster DAGs from Interventions

2026-10-08

AI Summary

This study addresses the inefficiency of edge learning in clustered directed acyclic graphs (DAGs) for causal abstraction by proposing COARSE. Under linear Gaussian assumptions, this method leverages interventional data to identify a clustered causal order and introduces the first score-based framework for clustered DAG learning. By integrating local search with cluster-level Bayesian Information Criterion (BIC) scoring, it efficiently recovers edge structures. Theoretically, COARSE achieves polynomial time complexity and statistical consistency. Empirically, it attains state-of-the-art accuracy on both synthetic and real-world datasets while accelerating edge learning by two orders of magnitude.

Abstract

Graphical approaches to causal abstraction transform a low-level causal directed acyclic graph (DAG) over many measured variables into a smaller, high-level DAG whose nodes cluster the original variables and whose edges summarize the causal relations between clusters. Such cluster DAGs are easier to interpret, but learning them requires finding the clusters and recovering the edges between them. Madaleno et al. (2026) learn the interventional coarsening (the cluster DAG that merges variables the interventions cannot distinguish) in two constraint-based phases: first the clusters, then the edges. We introduce COARSE, the first score-based method for this task: it keeps the two-phase structure but, under linear Gaussian assumptions, swaps the constraint-based edge phase for a score-based one. We show that the interventions themselves identify a causal order over the clusters, and learning the edges reduces to a single local search per cluster under a cluster-level BIC score. We prove that the procedure runs in polynomial time and, provided the variables affected by each intervention are correctly identified, that it is consistent. On synthetic and real-world interventional data, COARSE matches state-of-the-art edge recovery given enough samples, with an edge phase up to two orders of magnitude faster, including on dense graphs with hundreds of nodes.

Problem

• causal abstraction
• cluster DAG
• interventional data
• score-based learning
• causal discovery

Innovation

• Score-Based Learning
• Cluster DAGs
• Causal Abstraction
• Interventions
• BIC Score