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An explicit link between graphical models and Gaussian Markov random fields on metric graphs

Bolin, David LU ; Simas, Alexandre B. LU and Wallin, Jonas LU (2026) In Stochastic Processes and their Applications 196.
Abstract

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. This graphical model has a distribution which is faithful to its pairwise independence graph, that 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.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gaussian process, GMRF, Graphical models, Markov, Metric graph
in
Stochastic Processes and their Applications
volume
196
article number
104925
publisher
Elsevier
external identifiers
  • scopus:105032385244
ISSN
0304-4149
DOI
10.1016/j.spa.2026.104925
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2026 Elsevier B.V.
id
eca7ced3-514f-49d5-98a8-4540c01f5fd8
date added to LUP
2026-04-27 15:48:39
date last changed
2026-04-27 15:49:50
@article{eca7ced3-514f-49d5-98a8-4540c01f5fd8,
  abstract     = {{<p>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. This graphical model has a distribution which is faithful to its pairwise independence graph, that 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.</p>}},
  author       = {{Bolin, David and Simas, Alexandre B. and Wallin, Jonas}},
  issn         = {{0304-4149}},
  keywords     = {{Gaussian process; GMRF; Graphical models; Markov; Metric graph}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Stochastic Processes and their Applications}},
  title        = {{An explicit link between graphical models and Gaussian Markov random fields on metric graphs}},
  url          = {{http://dx.doi.org/10.1016/j.spa.2026.104925}},
  doi          = {{10.1016/j.spa.2026.104925}},
  volume       = {{196}},
  year         = {{2026}},
}