DROPS

Document

DOI: 10.4230/LIPIcs.CSL.2026.11

A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures

Authors: Mateo Torres-Ruiz, Robin Piedeleu, Alexandra Silva, and Fabio Zanasi

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

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.

Cite as

Mateo Torres-Ruiz, Robin Piedeleu, Alexandra Silva, and Fabio Zanasi. A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{torresruiz_et_al:LIPIcs.CSL.2026.11,
  author =	{Torres-Ruiz, Mateo and Piedeleu, Robin and Silva, Alexandra and Zanasi, Fabio},
  title =	{{A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.11},
  URN =		{urn:nbn:de:0030-drops-254358},
  doi =		{10.4230/LIPIcs.CSL.2026.11},
  annote =	{Keywords: String diagrams, Category theory, Mixture models, Probability theory}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.20

On Iteration in Discrete Probabilistic Programming

Authors: Mateo Torres-Ruiz, Robin Piedeleu, Alexandra Silva, and Fabio Zanasi

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

Discrete probabilistic programming languages provide an expressive tool for representing and reasoning about probabilistic models. These languages typically define the semantics of a program through its posterior distribution, obtained through exact inference techniques. While the semantics of standard programming constructs in this context is well understood, there is a gap in extending these languages with tools to reason about the asymptotic behaviour of programs. In this paper, we introduce unbounded iteration in the context of a discrete probabilistic programming language, give it a semantics, and show how to compute it exactly. This allows us to express the stationary distribution of a probabilistic function while preserving the efficiency of exact inference techniques. We discuss the advantages and limitations of our approach, showcasing their practical utility by considering examples where bounded iteration poses a challenge due to the inherent difficulty of assessing the proximity of a distribution to its stationary point.

Cite as

Mateo Torres-Ruiz, Robin Piedeleu, Alexandra Silva, and Fabio Zanasi. On Iteration in Discrete Probabilistic Programming. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{torresruiz_et_al:LIPIcs.FSCD.2024.20,
  author =	{Torres-Ruiz, Mateo and Piedeleu, Robin and Silva, Alexandra and Zanasi, Fabio},
  title =	{{On Iteration in Discrete Probabilistic Programming}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.20},
  URN =		{urn:nbn:de:0030-drops-203490},
  doi =		{10.4230/LIPIcs.FSCD.2024.20},
  annote =	{Keywords: Probabilistic programming, Programming languages semantics, Unbounded iteration}
}

Search Results

Documents authored by Torres-Ruiz, Mateo

A Complete Diagrammatic Calculus for Conditional Gaussian Mixtures

Abstract

Cite as

On Iteration in Discrete Probabilistic Programming

Abstract

Cite as

Thanks for your feedback!

Could not send message