On the Relationship between Bayesian Networks and Probabilistic Structural Causal Models

Computer Science > Artificial Intelligence [Submitted on 28 Mar 2026] On the Relationship between Bayesian Networks and Probabilistic Structural Causal Models Peter J.F. Lucas, Eleanora Zullo, Fabio Stella In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on structural equations or functions, that can be provided with uncertainty by adding independent, unobserved random variables to the models, equipped with probability distributions. One question that arises is whether a Bayesian network that has obtained from expert knowledge or learnt from data can be mapped to a probabilistic structural causal model, and whether or not this has consequences for the network structure and probability distribution. We show that linear algebra and linear programming offer key methods for the transformation, and examine properties for the existence and uniqueness of solutions based on dimensions of the probabilistic structural model. Finally, we examine in what way the semantics of the models is affected by this transformation. Keywords: Causality, probabilistic structural causal models, Bayesian networks, linear algebra, experimental software. Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG) Cite as: arXiv:2603.27406 [cs.AI]   (or arXiv:2603.27406v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.27406 Focus to learn more Submission history From: Peter Lucas [view email] [v1] Sat, 28 Mar 2026 20:59:39 UTC (96 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)