mlsanityData to 7 Oct 2026

Causal Consistency of Structural Equation Models

arXiv 1707.00819 ↗First posted 4 Jul 2017stat.ML cs.AI cs.LGcited by 114

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Abstract (arXiv)

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.

Key facts. Cited by 114 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jul 2017.

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Citing papers per year: 2021: 7; 2022: 14; 2023: 23; 2024: 15; 2025: 29; 2026: 26.

114 papers.

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  1. 2021Causal Abstractions of Neural Networkscited by 401
  2. 2021Towards Causal Representation Learningcited by 207
  3. 2023Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representationscited by 197
  4. 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretabilitycited by 194
  5. 2022Weakly supervised causal representation learningcited by 140
  6. 2021Inducing Causal Structure for Interpretable Neural Networkscited by 107
  7. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  8. 2023Interpretability at Scale: Identifying Causal Mechanisms in Alpacacited by 102
  9. 2022Amortized Inference for Causal Structure Learningcited by 89
  10. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  11. 2022From Statistical to Causal Learningcited by 40
  12. 2022Causal Effect Identification in Cluster DAGscited by 33
38 more
  1. 2021Compositional Abstraction Error and a Category of Causal Modelscited by 32
  2. 2025Everything, Everywhere, All at Once: Is Mechanistic Interpretability Identifiable?cited by 32
  3. 2024Unifying Causal Representation Learning with the Invariance Principlecited by 30
  4. 2022Causal Abstraction with Soft Interventionscited by 23
  5. 2022Causal Inference Through the Structural Causal Marginal Problemcited by 22
  6. 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
  7. 2026Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behaviorcited by 22
  8. 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributionscited by 21
  9. 2023Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimationcited by 20
  10. 2023Causal Modeling with Stationary Diffusionscited by 19
  11. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
  12. 2023Targeted Reduction of Causal Modelscited by 15
  13. 2022Abstraction between Structural Causal Models: A Review of Definitions and Propertiescited by 14
  14. 2026Sensorimotor World Models: Perception for Action via Inverse Dynamicscited by 14
  15. 2022On the Equivalence of Causal Models: A Category-Theoretic Approachcited by 13
  16. 2023Causal Optimal Transport of Abstractionscited by 13
  17. 2023Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractionscited by 11
  18. 2024Position: An Inner Interpretability Framework for AI Inspired by Lessons from Cognitive Neurosciencecited by 11
  19. 2025Internal Causal Mechanisms Robustly Predict Language Model Out-of-Distribution Behaviorscited by 11
  20. 2025How Causal Abstraction Underpins Computational Explanationcited by 10
  21. 2022Towards a Grounded Theory of Causation for Embodied AIcited by 9
  22. 2024What type of inference is planning?cited by 9
  23. 2025Causal Abstraction Learning based on the Semantic Embedding Principlecited by 9
  24. 2023A Measure-Theoretic Axiomatisation of Causalitycited by 8
  25. 2024Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confoundingcited by 8
  26. 2025ExoPredicator: Learning Abstract Models of Dynamic Worlds for Robot Planningcited by 8
  27. 2026Causality is Key for Interpretability Claims to Generalisecited by 8
  28. 2021Causal Modeling With Infinitely Many Variablescited by 7
  29. 2021Reasoning About Causal Models With Infinitely Many Variablescited by 7
  30. 2022Phenomenological Causalitycited by 7
  31. 2023Quantifying Consistency and Information Loss for Causal Abstraction Learningcited by 6
  32. 2023Interventionally Consistent Surrogates for Agent-based Simulatorscited by 6
  33. 2024Aligning Graphical and Functional Causal Abstractionscited by 6
  34. 2025What is causal about causal models and representations?cited by 6
  35. 2025Sample-efficient Learning of Concepts with Theoretical Guarantees: from Data to Concepts without Interventionscited by 6
  36. 2026Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world modelscited by 6
  37. 2023Meaningful Causal Aggregation and Paradoxical Confoundingcited by 5
  38. 2024Causally Abstracted Multi-armed Banditscited by 5

50 most cited of 114 All 114 (JSON)