mlsanityData to 7 Oct 2026

A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

arXiv 1908.07021 ↗First posted 19 Aug 2019math.ST cs.LO math.CTcited by 55

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Abstract (arXiv)

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

Key facts. Cited by 55 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Aug 2019.

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Citing papers per year: 2021: 7; 2022: 5; 2023: 12; 2024: 3; 2025: 12; 2026: 16.

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  1. 2022Weakly supervised causal representation learningcited by 140
  2. 2021Category Theory in Machine Learningcited by 36
  3. 2021Compositional Abstraction Error and a Category of Causal Modelscited by 32
  4. 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributionscited by 21
  5. 2022The d-separation criterion in Categorical Probabilitycited by 12
  6. 2023Going Beyond Neural Network Feature Similarity: The Network Feature Complexity and Its Interpretation Using Category Theorycited by 12
  7. 2025Large Causal Models from Large Language Modelscited by 8
  8. 2023Categorical Foundations of Explainable AI: A Unifying Theorycited by 7
  9. 2023Quantifying Consistency and Information Loss for Causal Abstraction Learningcited by 6
  10. 2023Beyond Boundaries: A Comprehensive Survey of Transferable Attacks on AI Systemscited by 6
  11. 2021Interpreting Dynamical Systems as Bayesian Reasonerscited by 5
  12. 2021A Categorical Semantics of Fuzzy Concepts in Conceptual Spacescited by 4
38 more
  1. 2024Reinforcement Learning in Categorical Cyberneticscited by 4
  2. 2024A Pattern Language for Machine Learning Taskscited by 4
  3. 2025Intuitionistic j-Do-Calculus in Topos Causal Modelscited by 4
  4. 2026Actionable Interpretability Must Be Defined in Terms of Symmetriescited by 4
  5. 2023The Compositional Structure of Bayesian Inferencecited by 3
  6. 2023A Category-theoretical Meta-analysis of Definitions of Disentanglementcited by 3
  7. 2023Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energycited by 3
  8. 2021Compositional Semantics for Probabilistic Programs with Exact Conditioningcited by 2
  9. 2022Compositional Active Inference II: Polynomial Dynamics. Approximate Inference Doctrinescited by 2
  10. 2023Enriching Disentanglement: From Logical Definitions to Quantitative Metricscited by 2
  11. 2025A Markov Categorical Framework for Language Modelingcited by 2
  12. 2025Topos Theory for Generative AI and LLMscited by 2
  13. 2026Causal Density Functionscited by 2
  14. 2026Odds Law: The Decomposition Algebra On How Intelligence Organizes Itself to Solve Difficult Problems Reliablycited by 2
  15. 2026Infinitesimal Causalitycited by 2
  16. 2021Generalized Optimization: A First Step Towards Category Theoretic Learning Theorycited by 1
  17. 2021A category theory framework for Bayesian learningcited by 1
  18. 2023Computing with Categories in Machine Learningcited by 1
  19. 2025An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Modelscited by 1
  20. 2025A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Modelscited by 1
  21. 2025Universal Reinforcement Learning in Coalgebras: Asynchronous Stochastic Computation via Conductioncited by 1
  22. 2026A Unifying Framework for Unsupervised Concept Extractioncited by 1
  23. 2022Markov categories, causal theories, and the do-calculuscited by 0
  24. 2022A Probabilistic Generative Model of Free Categoriescited by 0
  25. 2023String Diagrams with Factorized Densitiescited by 0
  26. 2023Overdrawing Urns using Categories of Signed Probabilitiescited by 0
  27. 2024SymDiff: Equivariant Diffusion via Stochastic Symmetrisationcited by 0
  28. 2025Categorical and geometric methods in statistical, manifold, and machine learningcited by 0
  29. 2025Topos Causal Modelscited by 0
  30. 2025Consciousness as a Functorcited by 0
  31. 2025Causal Abstractions, Categorically Unifiedcited by 0
  32. 2025Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspectivecited by 0
  33. 2026Categorical Belief Propagation: Sheaf-Theoretic Inference via Descent and Holonomycited by 0
  34. 2026CSQL: Mapping Documents into Causal Databasescited by 0
  35. 2026Notes on Forr'e's Notion of Conditional Independence and Causal Calculus for Continuous Variablescited by 0
  36. 2026From Intent to Evidence: A Categorical Approach for Structural Evaluation of Deep Research Agentscited by 0
  37. 2026MOCA: A Transformer-based Modular Causal Inference Framework with One-way Cross-attention and Cutting Feedbackcited by 0
  38. 2026A Contractive Feedback Semantics for Reinforcement Learningcited by 0

50 most cited of 55 All 55 (JSON)