### Abstract

Let X_{i}, i 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 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 V form a Markov chain, it is known that the I - Measure is always nonnegative [3]. We prove that Markov chain is essentially the only MRF that possesses this property. Our work is built on the set-theoretic characterization of an MRF in [4]. Unlike most works in the literature, we do not make the standard assumption that the underlying probability distribution is factorizable with respect to the graph representing the MRF.

Original language | English (US) |
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Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3040-3044 |

Number of pages | 5 |

ISBN (Electronic) | 9781509040964 |

DOIs | |

State | Published - Aug 9 2017 |

Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
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Country | Germany |

City | Aachen |

Period | 6/25/17 → 6/30/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2017 IEEE International Symposium on Information Theory, ISIT 2017*(pp. 3040-3044). [8007088] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8007088