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An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models

Authors Antonio Lorenzin , Fabio Zanasi

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LIPIcs.CALCO.2025.6.pdf
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ACM Subject Classification
  • Mathematics of computing → Probabilistic representations
Keywords
  • Functorial Semantics
  • Probabilistic Model
  • Bayesian Network

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Abstract

Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov network (an undirected model), whereas triangulation works in the opposite direction. We present a categorical framework where these transformations are modelled as functors between a category of Bayesian networks and one of Markov networks. The two kinds of network (the objects of these categories) are themselves represented as functors, from a "syntax" domain to a "semantics" codomain. Notably, moralisation and triangulation are definable inductively on such syntax, and operate as a form of functor pre-composition. This approach introduces a modular, algebraic perspective in the theory of probabilistic graphical models.

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Antonio Lorenzin and Fabio Zanasi. An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CALCO.2025.6

Author Details

Antonio Lorenzin
  • Computer Science Department, University College London, UK
Fabio Zanasi
  • Computer Science Department, University College London, UK

Funding

Our work has been supported by the ARIA Safeguarded AI TA1.1 programme.

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