ArticleEntropy (Basel, Switzerland)2020
On a Class of Tensor Markov Fields.
Article in Entropy (Basel, Switzerland), 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- An Information Theoretical Multilayer Network Approach to Breast Cancer Transcriptional Regulation.Frontiers in genetics · 2021Article
- Data Science: Measuring Uncertainties.Entropy (Basel, Switzerland) · 2020Article
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Abstract
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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