On Information-Theoretic Characterizations of Markov Random Fields and Subfields
| Autor: | Qi Chen, Chao Chen, Raymond W. Yeung, Pierre Moulin, Ali Al-Bashabsheh |
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| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Markov random field Random field Discrete Mathematics (cs.DM) Markov chain Computer Science - Information Theory Information Theory (cs.IT) 020206 networking & telecommunications 02 engineering and technology Library and Information Sciences Electronic mail Computer Science Applications Information diagram Combinatorics Conditional independence Computer Science::Computer Vision and Pattern Recognition 0202 electrical engineering electronic engineering information engineering Graph (abstract data type) Random variable Computer Science - Discrete Mathematics Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 65:1493-1511 |
| ISSN: | 1557-9654 0018-9448 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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