1. On Information-Theoretic Characterizations of Markov Random Fields and Subfields.
- Author
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Yeung, Raymond W., Al-Bashabsheh, Ali, Chen, Chao, Chen, Qi, and Moulin, Pierre
- Subjects
MARKOV random fields ,MARKOV processes ,FERROMAGNETIC materials ,SOCIAL network theory ,DISTRIBUTION (Probability theory) - 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]
- Published
- 2019
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