mlsanityData to 7 Oct 2026

Score-Based Learning of Cluster DAGs from Interventions

arXiv 2610.11947 ↗First posted 8 Oct 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 22 of its 81 references that are in the map. First posted on arXiv 8 Oct 2026.

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References · 22

  1. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 533
  2. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  3. 2017Causal Consistency of Structural Equation Modelscited by 114
  4. 2019Permutation-Based Causal Structure Learning with Unknown Intervention Targetscited by 69
  5. 2013Causal Networks: Semantics and Expressivenesscited by 67
  6. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 63
  7. 2019Approximate Causal Abstractioncited by 62
  8. 2014Visual Causal Feature Learningcited by 59
  9. 2022Causal Abstraction with Soft Interventionscited by 23
  10. 2024Standardizing Structural Causal Modelscited by 17
  11. 2022Abstraction between Structural Causal Models: A Review of Definitions and Propertiescited by 14
  12. 2013On the Equivalence of Causal Modelscited by 13
10 more
  1. 2022Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventionscited by 12
  2. 2021Clustering and Structural Robustness in Causal Diagramscited by 10
  3. 2025Causal Abstraction Learning based on the Semantic Embedding Principlecited by 9
  4. 2025Embracing Discrete Search: A Reasonable Approach to Causal Structure Learningcited by 4
  5. 2026Structural Causal Bottleneck Modelscited by 4
  6. 2025Distributionally Robust Causal Abstractionscited by 3
  7. 2017Optimal Experiment Design for Causal Discovery from Fixed Number of Experimentscited by 2
  8. 2026Coarsening Causal DAG Modelscited by 2
  9. 2026Coarsening Linear Non-Gaussian Causal Models with Cyclescited by 2
  10. 2026I-FLOP: Fast Learning of Order and Parents from Interventional Datacited by 1

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