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On Information-Theoretic Characterizations of Markov Random Fields and Subfields.
- Source :
- IEEE Transactions on Information Theory; Mar2019, Vol. 65 Issue 3, p1493-1511, 19p
- Publication Year :
- 2019
-
Abstract
- Let $X_{i}, i~\in V$ 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 $X_{i}, i~\in V'$ 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 $X_{i}, i~\in V$ 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). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 134886969
- Full Text :
- https://doi.org/10.1109/TIT.2018.2866564