mlsanityData to 7 Oct 2026

Compositional Abstraction Error and a Category of Causal Models

arXiv 2103.15758 ↗First posted 29 Mar 2021stat.ML cs.AI cs.LGcited by 32

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Abstract (arXiv)

Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and make predictions about the variables upon intervening on the system. Yet, it is difficult to formalise how we may change the underlying variables used to describe the system, say moving from fine-grained to coarse-grained variables. Here, we argue that compositionality is a desideratum for such model transformations and the associated errors: When abstracting a reference model M iteratively, first obtaining M' and then further simplifying that to obtain M'', we expect the composite transformation from M to M'' to exist and its error to be bounded by the errors incurred by each individual transformation step. Category theory, the study of mathematical objects via compositional transformations between them, offers a natural language to develop our framework for model transformations and abstractions. We introduce a category of finite interventional causal models and, leveraging theory of enriched categories, prove the desired compositionality properties for our framework.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). Builds on 12 of its 47 references that are in the map. First posted on arXiv 29 Mar 2021.

Builds on

12 of 47 references.

References · 12

  1. 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
  2. 2017Causal Consistency of Structural Equation Modelscited by 114
  3. 2018Abstracting Causal Modelscited by 104
  4. 2019Approximate Causal Abstractioncited by 62
  5. 2014Visual Causal Feature Learningcited by 59
  6. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 55
  7. 2018Causal Inference by String Diagram Surgerycited by 23
  8. 2016When the map is better than the territorycited by 17
  9. 2016Causal Discovery from Subsampled Time Series Data by Constraint Optimizationcited by 12
  10. 2020Causal Feature Learning for Utility-Maximizing Agentscited by 5
  11. 2015MERLiN: Mixture Effect Recovery in Linear Networkscited by 2
  12. 2020The algebra and machine representation of statistical modelscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 11; 2024: 3; 2025: 8; 2026: 5.

32 papers.

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  1. 2023Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representationscited by 197
  2. 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretabilitycited by 194
  3. 2022Causal Abstraction with Soft Interventionscited by 23
  4. 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributionscited by 21
  5. 2023Targeted Reduction of Causal Modelscited by 15
  6. 2022Abstraction between Structural Causal Models: A Review of Definitions and Propertiescited by 14
  7. 2023Causal models in string diagramscited by 14
  8. 2023Causal Optimal Transport of Abstractionscited by 13
  9. 2022The d-separation criterion in Categorical Probabilitycited by 12
  10. 2021Context-Specific Causal Discovery for Categorical Data Using Staged Treescited by 10
  11. 2024Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challengescited by 8
  12. 2023Quantifying Consistency and Information Loss for Causal Abstraction Learningcited by 6
20 more
  1. 2023Interventionally Consistent Surrogates for Agent-based Simulatorscited by 6
  2. 2024Aligning Graphical and Functional Causal Abstractionscited by 6
  3. 2025What is causal about causal models and representations?cited by 6
  4. 2023Meaningful Causal Aggregation and Paradoxical Confoundingcited by 5
  5. 2024Causally Abstracted Multi-armed Banditscited by 5
  6. 2025Combining Causal Models for More Accurate Abstractions of Neural Networkscited by 4
  7. 2022Towards Computing an Optimal Abstraction for Structural Causal Modelscited by 3
  8. 2025Distributionally Robust Causal Abstractionscited by 3
  9. 2025Modeling Discrimination with Causal Abstractioncited by 2
  10. 2023Axiomatization of Interventional Probability Distributionscited by 1
  11. 2023CASR: Refining Action Segmentation via Marginalizing Frame-levle Causal Relationshipscited by 1
  12. 2025On the Identifiability of Causal Abstractionscited by 1
  13. 2025Identifiability in Causal Abstractions: A Hierarchy of Criteriacited by 1
  14. 2025Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policiescited by 1
  15. 2025Causal Feature Learning in the Social Sciencescited by 0
  16. 2026Multi-Level Causal Embeddingscited by 0
  17. 2026Causal Foundations of Collective Agencycited by 0
  18. 2026Validating Causal Abstraction Metrics on Simulated Complex Systemscited by 0
  19. 2026Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcomecited by 0
  20. 2026What Can a Leaderboard Certify? Compositional Controllability for Fair Evaluation and Training of Biomedical Literature-Review Agentscited by 0