A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures

Reference. A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures

We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones, follow a multivariate Gaussian distribution. This setting includes important families of distributions such as Gaussian mixtures, where each Gaussian component is selected according to a discrete variable. We develop a string diagrammatic syntax for distributions of this type, give it a compositional semantics, and equip it with a sound and complete equational theory that characterises when two mixtures represent the same distribution.

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Cite as @torresruiz-2026-a (helia, typst) · \cite{torresruiz-2026-a} (LaTeX)

BibTeX

bibtex · 14 lines

@inproceedings{torresruiz-2026-a,
  doi = {10.4230/LIPICS.CSL.2026.11},
  url = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.11},
  author = {Torres-Ruiz, Mateo and Piedeleu, Robin and Silva, Alexandra and Zanasi, Fabio},
  keywords = {String diagrams, Category theory, Mixture models, Probability theory, Theory of computation → Categorical semantics, Theory of computation → Logic},
  language = {en},
  title = {A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures},
  volume = {363},
  pages = {11:1-11:17},
  publisher = {Schloss Dagstuhl – Leibniz-Zentrum für Informatik},
  year = {2026},
  copyright = {Creative Commons Attribution 4.0 International license},
  booktitle = {34th EACSL Annual Conference on Computer Science Logic (CSL 2026)}
}

hayagriva YAML (typst)

yaml · 18 lines

torresruiz-2026-a:
  type: article
  title: A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures
  author:
  - Torres-Ruiz, Mateo
  - Piedeleu, Robin
  - Silva, Alexandra
  - Zanasi, Fabio
  date: 2026
  page-range: 11:1-11:17
  url: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.11
  serial-number:
    doi: 10.4230/LIPICS.CSL.2026.11
  parent:
    type: proceedings
    title: 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)
    publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
    volume: 363

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Categories for the Working Mathematician maclane_19711971

Web

External (23)

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