On information-theoretic characterizations of markov random fields and subfields

Raymond W. Yeung, Ali Al-Bashabsheh, Chao Chen, Qi Chen, Pierre Moulin

Research output: Contribution to journalArticle

Abstract

Let X i , i ϵ V form a Markov random field (MRF) represented by an undirected graph G = (V,E) , and V′ be a subset of V. We determine the smallest graph that can always represent the subfield X i , i ϵ V′ as an MRF. Based on this result, we obtain a necessary and sufficient condition for a subfield of a Markov tree to be also a Markov tree. When G is a path so that X i , i ϵ V form a Markov chain, it is known that the I -Measure is always nonnegative (Kawabata and Yeung in 1992). We prove that Markov chain is essentially the only MRF such that the I -Measure is always nonnegative. By applying our characterization of the smallest graph representation of a subfield of an MRF, we develop a recursive approach for constructing information diagrams for MRFs. Our work is built on the set-theoretic characterization of an MRF (Yeung et al. in 2002).

Original languageEnglish (US)
Article number8444473
Pages (from-to)1493-1511
Number of pages19
JournalIEEE Transactions on Information Theory
Volume65
Issue number3
DOIs
StatePublished - Mar 2019

Keywords

  • I-Measure
  • Markov random field
  • conditional independence
  • information diagram
  • subfield

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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