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On a Class of Tensor Markov Fields

Here, we introduce a class of Tensor Markov Fields intended as probabilistic graphical models from random variables spanned over multiplexed contexts. These fields are an extension of Markov Random Fields for tensor-valued random variables. By extending the results of Dobruschin, Hammersley and Clif...

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Detalles Bibliográficos
Autor principal: Hernández-Lemus, Enrique
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516931/
https://www.ncbi.nlm.nih.gov/pubmed/33286225
http://dx.doi.org/10.3390/e22040451
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author Hernández-Lemus, Enrique
author_facet Hernández-Lemus, Enrique
author_sort Hernández-Lemus, Enrique
collection PubMed
description Here, we introduce a class of Tensor Markov Fields intended as probabilistic graphical models from random variables spanned over multiplexed contexts. These fields are an extension of Markov Random Fields for tensor-valued random variables. By extending the results of Dobruschin, Hammersley and Clifford to such tensor valued fields, we proved that tensor Markov fields are indeed Gibbs fields, whenever strictly positive probability measures are considered. Hence, there is a direct relationship with many results from theoretical statistical mechanics. We showed how this class of Markov fields it can be built based on a statistical dependency structures inferred on information theoretical grounds over empirical data. Thus, aside from purely theoretical interest, the Tensor Markov Fields described here may be useful for mathematical modeling and data analysis due to their intrinsic simplicity and generality.
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spelling pubmed-75169312020-11-09 On a Class of Tensor Markov Fields Hernández-Lemus, Enrique Entropy (Basel) Article Here, we introduce a class of Tensor Markov Fields intended as probabilistic graphical models from random variables spanned over multiplexed contexts. These fields are an extension of Markov Random Fields for tensor-valued random variables. By extending the results of Dobruschin, Hammersley and Clifford to such tensor valued fields, we proved that tensor Markov fields are indeed Gibbs fields, whenever strictly positive probability measures are considered. Hence, there is a direct relationship with many results from theoretical statistical mechanics. We showed how this class of Markov fields it can be built based on a statistical dependency structures inferred on information theoretical grounds over empirical data. Thus, aside from purely theoretical interest, the Tensor Markov Fields described here may be useful for mathematical modeling and data analysis due to their intrinsic simplicity and generality. MDPI 2020-04-16 /pmc/articles/PMC7516931/ /pubmed/33286225 http://dx.doi.org/10.3390/e22040451 Text en © 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Hernández-Lemus, Enrique
On a Class of Tensor Markov Fields
title On a Class of Tensor Markov Fields
title_full On a Class of Tensor Markov Fields
title_fullStr On a Class of Tensor Markov Fields
title_full_unstemmed On a Class of Tensor Markov Fields
title_short On a Class of Tensor Markov Fields
title_sort on a class of tensor markov fields
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516931/
https://www.ncbi.nlm.nih.gov/pubmed/33286225
http://dx.doi.org/10.3390/e22040451
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