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.
View on arXiv@article{lorenzin2025_2503.11820,
title={ An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models },
author={ Antonio Lorenzin and Fabio Zanasi },
journal={arXiv preprint arXiv:2503.11820},
year={ 2025 }
}