An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915415614029824 |
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| author | Lorenzin, Antonio Zanasi, Fabio |
| author_facet | Lorenzin, Antonio Zanasi, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models Lorenzin, Antonio Zanasi, Fabio Artificial Intelligence Logic in Computer Science Category Theory 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. |
| title | An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models |
| topic | Artificial Intelligence Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2503.11820 |