mlsanityData to 14 Oct 2026

Abstraction between Structural Causal Models: A Review of Definitions and Properties

arXiv 2207.08603 ↗First posted 18 Jul 2022cs.AI cs.LGcited by 15

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Abstract (arXiv)

Structural causal models (SCMs) are a widespread formalism to deal with causal systems. A recent direction of research has considered the problem of relating formally SCMs at different levels of abstraction, by defining maps between SCMs and imposing a requirement of interventional consistency. This paper offers a review of the solutions proposed so far, focusing on the formal properties of a map between SCMs, and highlighting the different layers (structural, distributional) at which these properties may be enforced. This allows us to distinguish families of abstractions that may or may not be permitted by choosing to guarantee certain properties instead of others. Such an understanding not only allows to distinguish among proposal for causal abstraction with more awareness, but it also allows to tailor the definition of abstraction with respect to the forms of abstraction relevant to specific applications.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 8 of its 15 references that are in the map. First posted on arXiv 18 Jul 2022.

Builds on

8 of 15 references.

References · 8

  1. 2021Towards Causal Representation Learningcited by 209
  2. 2017Causal Consistency of Structural Equation Modelscited by 118
  3. 2018Abstracting Causal Modelscited by 107
  4. 2019Approximate Causal Abstractioncited by 63
  5. 2021Compositional Abstraction Error and a Category of Causal Modelscited by 33
  6. 2013Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphscited by 25
  7. 2018Causal Inference by String Diagram Surgerycited by 24
  8. 2022On the Equivalence of Causal Models: A Category-Theoretic Approachcited by 13

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 5; 2025: 2; 2026: 4.

15 papers.

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  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  2. 2022Causal Abstraction with Soft Interventionscited by 23
  3. 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributionscited by 23
  4. 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
  5. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  6. 2024Learning Causal Abstractions of Linear Structural Causal Modelscited by 11
  7. 2025How Causal Abstraction Underpins Computational Explanationcited by 11
  8. 2024Causally Abstracted Multi-armed Banditscited by 6
  9. 2024Causal Abstraction in Model Interpretability: A Compact Surveycited by 2
  10. 2024Factored space models: Towards causality between levels of abstractioncited by 1
  11. 2025On the Identifiability of Causal Abstractionscited by 1
  12. 2026CLAM: Causal Spatial Disaggregation to Infer Local Effects From Coarse Datacited by 1
3 more
  1. 2026Tracking Equivalent Mechanistic Interpretations Across Neural Networkscited by 0
  2. 2026Validating Causal Abstraction Metrics on Simulated Complex Systemscited by 0
  3. 2026Score-Based Learning of Cluster DAGs from Interventionscited by 0