mlsanityData to 14 Oct 2026

Aligning Graphical and Functional Causal Abstractions

arXiv 2412.17080 ↗First posted 22 Dec 2024cs.AIcited by 6

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Abstract (arXiv)

Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like α-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent α-abstractions with the range of abstracted variables mapped bijectively, and constructive τ-abstractions. Furthermore, we extend this alignment and the expressivity of graphical abstractions by introducing Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 14 of its 21 references that are in the map. First posted on arXiv 22 Dec 2024.

Builds on

14 of 21 references.

References · 14

  1. 2021Causal Abstractions of Neural Networkscited by 422
  2. 2017Causal Consistency of Structural Equation Modelscited by 118
  3. 2018Abstracting Causal Modelscited by 107
  4. 2021Compositional Abstraction Error and a Category of Causal Modelscited by 33
  5. 2022Causal Abstraction with Soft Interventionscited by 23
  6. 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributionscited by 23
  7. 2023Foundations of Causal Discovery on Groups of Variablescited by 22
  8. 2024Neural Causal Abstractionscited by 21
  9. 2023Targeted Reduction of Causal Modelscited by 15
  10. 2023Causal Optimal Transport of Abstractionscited by 13
  11. 2015Learning Structures of Bayesian Networks for Variable Groupscited by 12
  12. 2024Learning Causal Abstractions of Linear Structural Causal Modelscited by 11
2 more
  1. 2023Interventionally Consistent Surrogates for Agent-based Simulatorscited by 6
  2. 2024Causally Abstracted Multi-armed Banditscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 2.

6 papers.

  1. 2025Causal Abstraction Learning based on the Semantic Embedding Principlecited by 9
  2. 2026Coarsening Causal DAG Modelscited by 4
  3. 2025Distributionally Robust Causal Abstractionscited by 3
  4. 2025Cluster-Dags as Powerful Background Knowledge For Causal Discoverycited by 2
  5. 2025Using causal abstractions to accelerate decision-making in complex bandit problemscited by 1
  6. 2026Multi-Level Causal Embeddingscited by 0