2025/01/07 by David Bolin, Bolin, David, Alexandre B. Simas +3
Computer Science · #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Mathematics #Graph Theory and Algorithms #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2501.03701
openalex publication_date 2025/01/07 · openalex created_date 2025/01/09 · openalex updated_date 2026/07/28
We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a Gaussian graphical model with a distribution which is faithful to its pairwise independence graph, which coincides with the neighbor structure of the metric graph. This is used to show that there are no Gaussian random fields on general metric graphs which are both Markov and isotropic in some suitably regular metric on the graph, such as the geodesic or resistance metrics.