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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2020
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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. |
format | Online Article Text |
id | pubmed-7516931 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT hernandezlemusenrique onaclassoftensormarkovfields |