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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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/4/451 |
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| author | Enrique Hernández-Lemus |
| author_facet | Enrique Hernández-Lemus |
| author_sort | Enrique Hernández-Lemus |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T20:25:53Z |
| format | Article |
| id | doaj.art-299cd16d237f45c5bdf020fac9e5d4af |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T20:25:53Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-299cd16d237f45c5bdf020fac9e5d4af2023-11-19T21:45:11ZengMDPI AGEntropy1099-43002020-04-0122445110.3390/e22040451On a Class of Tensor Markov FieldsEnrique Hernández-Lemus0Computational Genomics Division, National Institute of Genomic Medicine, 14610 Mexico City, MexicoHere, 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.https://www.mdpi.com/1099-4300/22/4/451Markov random fieldsprobabilistic graphical modelsmultilayer networks |
| spellingShingle | Enrique Hernández-Lemus On a Class of Tensor Markov Fields Entropy Markov random fields probabilistic graphical models multilayer networks |
| 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 | Markov random fields probabilistic graphical models multilayer networks |
| url | https://www.mdpi.com/1099-4300/22/4/451 |
| work_keys_str_mv | AT enriquehernandezlemus onaclassoftensormarkovfields |