mlsanityData to 7 Oct 2026

Disintegration and Bayesian Inversion via String Diagrams

arXiv 1709.00322 ↗First posted 29 Aug 2017cs.AIcited by 32

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Abstract (arXiv)

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Aug 2017.

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Citing papers per year: 2021: 6; 2022: 3; 2023: 11; 2024: 2; 2025: 6; 2026: 4.

32 papers.

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  11. 2023A Category-theoretical Meta-analysis of Definitions of Disentanglementcited by 3
  12. 2023Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energycited by 3
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  11. 2025A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Modelscited by 1
  12. 2022A Probabilistic Generative Model of Free Categoriescited by 0
  13. 2023Formalising and Learning a Quantum Model of Conceptscited by 0
  14. 2023String Diagrams with Factorized Densitiescited by 0
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