### 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) |
---|---|

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 |
---|---|

ISSN (Print) | 2157-8095 |

### Other

Other | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
---|---|

Country | Germany |

City | Aachen |

Period | 6/25/17 → 6/30/17 |

### Fingerprint

### ASJC Scopus subject areas

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

### 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

**Information-theoretic characterizations of Markov random fields and subfields.** / Yeung, Raymond W.; Al-Bashabsheh, Ali; Chen, Chao; Chen, Qi; Moulin, Pierre.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2017 IEEE International Symposium on Information Theory, ISIT 2017.*, 8007088, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 3040-3044, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8007088

}

TY - GEN

T1 - Information-theoretic characterizations of Markov random fields and subfields

AU - Yeung, Raymond W.

AU - Al-Bashabsheh, Ali

AU - Chen, Chao

AU - Chen, Qi

AU - Moulin, Pierre

PY - 2017/8/9

Y1 - 2017/8/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85034042959&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034042959&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8007088

DO - 10.1109/ISIT.2017.8007088

M3 - Conference contribution

AN - SCOPUS:85034042959

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 3040

EP - 3044

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -