On Functions of Markov Random Fields

Bernhard Geiger, Ali Al-Bashabsheh

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


We derive two sufficient conditions for a function of a Markov random field (MRF) on a given graph to be a MRF on the same graph. The first condition is information-theoretic and parallels a recent information-theoretic characterization of lumpability of Markov chains. The second condition, which is easier to check, is based on the potential functions of the corresponding Gibbs field. We illustrate our sufficient conditions at the hand of several examples and discuss implications for practical applications of MRFs. As a side result, we give a partial characterization of functions of MRFs that are information preserving.

Original languageEnglish
Title of host publication2020 IEEE Information Theory Workshop, ITW 2020
ISBN (Electronic)9781728159621
Publication statusPublished - 11 Apr 2021
Event2020 IEEE Information Theory Workshop: ITW 2020 - Virtuell, Italy
Duration: 11 Apr 202115 Apr 2021

Publication series

Name2020 IEEE Information Theory Workshop, ITW 2020


Conference2020 IEEE Information Theory Workshop
Abbreviated titleITW 2020


  • Gibbs field
  • Hidden Markov random field
  • Lumpability
  • Markov random field

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Theoretical Computer Science
  • Signal Processing
  • Computational Theory and Mathematics


Dive into the research topics of 'On Functions of Markov Random Fields'. Together they form a unique fingerprint.

Cite this