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On Information-Theoretic Characterizations of Markov Random Fields and Subfields
- Publication Year :
- 2016
-
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 and the information diagram assumes a very special structure Kawabata and Yeung (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 in Yeung, Lee, and Ye (2002).
- Subjects :
- Computer Science - Discrete Mathematics
Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1608.03697
- Document Type :
- Working Paper