Pairwise and uniformly hidden markov fields

Wojciech Pieczynski

doi:10.1063/1.3225271

Pairwise and uniformly hidden markov fields

Wojciech Pieczynski

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

Abstract

In Hidden Markov Fields (HMF) models there are two random fields: the hidden Markov field X and the observed field Y. In Pairwise Markov Fields (PMF) models one directly assumes the Markovianity of the couple (X, Y). PMF are more general than HMF; in fact, in PMF X is not necessarily Markovian. The aim of the paper is to provide some necessary and sufficient conditions under which PMF are HMF. We introduce the notion of "uniformly" HMF (UHMF) and we provide a general condition under which a PMF is an UHMF. Some interest of the presented results in the frame of Triplet Markov Fields (TMF) models, in which a third auxiliary random field is added and one considers the Markovianity of (X, U, Y), is also briefly discussed.

Original language	English
Title of host publication	Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008
Pages	193-196
Number of pages	4
DOIs	https://doi.org/10.1063/1.3225271
Publication status	Published - 1 Dec 2009
Event	6th International Conference on Computational Methods in Sciences and Engineering 2008, ICCMSE 2008 - Hersonissos, Crete, Greece Duration: 25 Sept 2008 → 30 Sept 2008

Publication series

Name	AIP Conference Proceedings
Volume	1148 2
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	6th International Conference on Computational Methods in Sciences and Engineering 2008, ICCMSE 2008
Country/Territory	Greece
City	Hersonissos, Crete
Period	25/09/08 → 30/09/08

Keywords

Pairwise Markov Fields
Triplet Markov fields
Uniformly Hidden Markov Fields

Access to Document

10.1063/1.3225271

Cite this

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title = "Pairwise and uniformly hidden markov fields",

abstract = "In Hidden Markov Fields (HMF) models there are two random fields: the hidden Markov field X and the observed field Y. In Pairwise Markov Fields (PMF) models one directly assumes the Markovianity of the couple (X, Y). PMF are more general than HMF; in fact, in PMF X is not necessarily Markovian. The aim of the paper is to provide some necessary and sufficient conditions under which PMF are HMF. We introduce the notion of {"}uniformly{"} HMF (UHMF) and we provide a general condition under which a PMF is an UHMF. Some interest of the presented results in the frame of Triplet Markov Fields (TMF) models, in which a third auxiliary random field is added and one considers the Markovianity of (X, U, Y), is also briefly discussed.",

keywords = "Pairwise Markov Fields, Triplet Markov fields, Uniformly Hidden Markov Fields",

author = "Wojciech Pieczynski",

year = "2009",

month = dec,

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doi = "10.1063/1.3225271",

language = "English",

isbn = "9780735406858",

series = "AIP Conference Proceedings",

pages = "193--196",

booktitle = "Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008",

note = "6th International Conference on Computational Methods in Sciences and Engineering 2008, ICCMSE 2008 ; Conference date: 25-09-2008 Through 30-09-2008",

}

Pieczynski, W 2009, Pairwise and uniformly hidden markov fields. in Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008. AIP Conference Proceedings, vol. 1148 2, pp. 193-196, 6th International Conference on Computational Methods in Sciences and Engineering 2008, ICCMSE 2008, Hersonissos, Crete, Greece, 25/09/08. https://doi.org/10.1063/1.3225271

Pairwise and uniformly hidden markov fields. / Pieczynski, Wojciech.
Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008. 2009. p. 193-196 (AIP Conference Proceedings; Vol. 1148 2).

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

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N2 - In Hidden Markov Fields (HMF) models there are two random fields: the hidden Markov field X and the observed field Y. In Pairwise Markov Fields (PMF) models one directly assumes the Markovianity of the couple (X, Y). PMF are more general than HMF; in fact, in PMF X is not necessarily Markovian. The aim of the paper is to provide some necessary and sufficient conditions under which PMF are HMF. We introduce the notion of "uniformly" HMF (UHMF) and we provide a general condition under which a PMF is an UHMF. Some interest of the presented results in the frame of Triplet Markov Fields (TMF) models, in which a third auxiliary random field is added and one considers the Markovianity of (X, U, Y), is also briefly discussed.

AB - In Hidden Markov Fields (HMF) models there are two random fields: the hidden Markov field X and the observed field Y. In Pairwise Markov Fields (PMF) models one directly assumes the Markovianity of the couple (X, Y). PMF are more general than HMF; in fact, in PMF X is not necessarily Markovian. The aim of the paper is to provide some necessary and sufficient conditions under which PMF are HMF. We introduce the notion of "uniformly" HMF (UHMF) and we provide a general condition under which a PMF is an UHMF. Some interest of the presented results in the frame of Triplet Markov Fields (TMF) models, in which a third auxiliary random field is added and one considers the Markovianity of (X, U, Y), is also briefly discussed.

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KW - Triplet Markov fields

KW - Uniformly Hidden Markov Fields

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M3 - Conference contribution

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BT - Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008

T2 - 6th International Conference on Computational Methods in Sciences and Engineering 2008, ICCMSE 2008

Y2 - 25 September 2008 through 30 September 2008

ER -

Pairwise and uniformly hidden markov fields

Abstract

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Keywords

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