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Open AccessArticle

On a Class of Tensor Markov Fields

1
Computational Genomics Division, National Institute of Genomic Medicine, 14610 Mexico City, Mexico
2
Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, 04510 Mexico City, Mexico
Entropy 2020, 22(4), 451; https://doi.org/10.3390/e22040451
Received: 6 March 2020 / Revised: 1 April 2020 / Accepted: 9 April 2020 / Published: 16 April 2020
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
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. View Full-Text
Keywords: Markov random fields; probabilistic graphical models; multilayer networks Markov random fields; probabilistic graphical models; multilayer networks
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Hernández-Lemus, E. On a Class of Tensor Markov Fields. Entropy 2020, 22, 451.

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