mlsanityData to 14 Oct 2026

A Measure-Theoretic Axiomatisation of Causality

arXiv 2305.17139 ↗First posted 19 May 2023cs.AI math.ST stat.THcited by 8

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Abstract (arXiv)

Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of textitwhat happens when one intervenes on a system, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a textitcausal space, consisting of a probability space along with a collection of transition probability kernels, called textitcausal kernels, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 28 of its 76 references that are in the map. First posted on arXiv 19 May 2023.

Builds on

28 of 76 references.

References · 28

  1. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  2. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  3. 2019Causality for Machine Learningcited by 243
  4. 2020Representation Learning via Invariant Causal Mechanismscited by 199
  5. 2021Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyondcited by 178
  6. 2022Weakly supervised causal representation learningcited by 140
  7. 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
  8. 2017Causal Consistency of Structural Equation Modelscited by 118
  9. 2018Abstracting Causal Modelscited by 107
  10. 2021Desiderata for Representation Learning: A Causal Perspectivecited by 76
  11. 2019Approximate Causal Abstractioncited by 63
  12. 2015A Modification of the Halpern-Pearl Definition of Causalitycited by 47
16 more
  1. 2022From Statistical to Causal Learningcited by 40
  2. 2020Causal models for dynamical systemscited by 34
  3. 2016From Deterministic ODEs to Dynamic Structural Causal Modelscited by 32
  4. 2021Causal Sufficiency and Actual Causationcited by 29
  5. 2018Causal Modeling of Dynamical Systemscited by 24
  6. 2018Causal Inference by String Diagram Surgerycited by 24
  7. 2020Probabilistic Reasoning across the Causal Hierarchycited by 19
  8. 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
  9. 2022Backtracking Counterfactualscited by 16
  10. 2022A Causal Analysis of Harmcited by 15
  11. 2022Quantifying Harmcited by 10
  12. 2022Towards a Grounded Theory of Causation for Embodied AIcited by 9
  13. 2021Causal Modeling With Infinitely Many Variablescited by 7
  14. 2014Subjectivity, Bayesianism, and Causalitycited by 2
  15. 2021Model Explanations via the Axiomatic Causal Lenscited by 1
  16. 2022Dilations and information flow axioms in categorical probabilitycited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 5; 2026: 1.

8 papers.

  1. 2025What is causal about causal models and representations?cited by 6
  2. 2025Measure-Theoretic Anti-Causal Representation Learningcited by 4
  3. 2025Algorithmic causal structure emerging through compressioncited by 3
  4. 2024Systems with Switching Causal Relations: A Meta-Causal Perspectivecited by 2
  5. 2025Probabilistic Modelling is Sufficient for Causal Inferencecited by 2
  6. 2024ExDAG: an MIQP Algorithm for Learning DAGscited by 1
  7. 2025A fine-grained look at causal effects in causal spacescited by 0
  8. 2026Orca: Neural Operators for Causal Reasoning in Continuous Timecited by 0