mlsanityData to 7 Oct 2026

The d-separation criterion in Categorical Probability

arXiv 2207.05740 ↗First posted 12 Jul 2022math.ST cs.LO math.CTcited by 12

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Abstract (arXiv)

The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability theory by introducing a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion. This approach has two main benefits. First, categorical d-separation is a very intuitive criterion based on topological connectedness. Second, our results apply both to measure-theoretic probability (with standard Borel spaces) and beyond probability theory, including to deterministic and possibilistic networks. It therefore provides a clean proof of the equivalence of local and global Markov properties with causal compatibility for continuous and mixed random variables as well as deterministic and possibilistic variables.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 11 of its 39 references that are in the map. First posted on arXiv 12 Jul 2022.

Builds on

11 of 39 references.

References · 11

  1. 2013Causal Networks: Semantics and Expressivenesscited by 67
  2. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 55
  3. 2017Disintegration and Bayesian Inversion via String Diagramscited by 32
  4. 2017Markov Properties for Graphical Models with Cycles and Latent Variablescited by 32
  5. 2021Compositional Abstraction Error and a Category of Causal Modelscited by 32
  6. 2013On the Testability of Causal Models with Latent and Instrumental Variablescited by 26
  7. 2018Causal Inference by String Diagram Surgerycited by 23
  8. 2013Instrumentality Tests Revisitedcited by 8
  9. 2022Free gs-monoidal categories and free Markov categoriescited by 6
  10. 2016Rewriting modulo symmetric monoidal structurecited by 4
  11. 2021Transitional Conditional Independencecited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 7; 2026: 2.

12 papers.

  1. 2023Causal models in string diagramscited by 14
  2. 2025Intuitionistic j-Do-Calculus in Topos Causal Modelscited by 4
  3. 2023Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energycited by 3
  4. 2025A "good regulator theorem" for embodied agentscited by 3
  5. 2026Infinitesimal Causalitycited by 2
  6. 2025A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Modelscited by 1
  7. 2023String Diagrams with Factorized Densitiescited by 0
  8. 2025Topos Causal Modelscited by 0
  9. 2025Consciousness as a Functorcited by 0
  10. 2025Causal Abstractions, Categorically Unifiedcited by 0
  11. 2025Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspectivecited by 0
  12. 2026Notes on Forr'e's Notion of Conditional Independence and Causal Calculus for Continuous Variablescited by 0