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Generalised Measures of Multivariate Information Content

The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted...

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Detalles Bibliográficos
Autores principales: Finn, Conor, Lizier, Joseph T.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851747/
https://www.ncbi.nlm.nih.gov/pubmed/33285991
http://dx.doi.org/10.3390/e22020216
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author Finn, Conor
Lizier, Joseph T.
author_facet Finn, Conor
Lizier, Joseph T.
author_sort Finn, Conor
collection PubMed
description The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a non-observing third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content.
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spelling pubmed-78517472021-02-24 Generalised Measures of Multivariate Information Content Finn, Conor Lizier, Joseph T. Entropy (Basel) Article The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a non-observing third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content. MDPI 2020-02-14 /pmc/articles/PMC7851747/ /pubmed/33285991 http://dx.doi.org/10.3390/e22020216 Text en © 2020 by the authors. 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
Finn, Conor
Lizier, Joseph T.
Generalised Measures of Multivariate Information Content
title Generalised Measures of Multivariate Information Content
title_full Generalised Measures of Multivariate Information Content
title_fullStr Generalised Measures of Multivariate Information Content
title_full_unstemmed Generalised Measures of Multivariate Information Content
title_short Generalised Measures of Multivariate Information Content
title_sort generalised measures of multivariate information content
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851747/
https://www.ncbi.nlm.nih.gov/pubmed/33285991
http://dx.doi.org/10.3390/e22020216
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