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Conditional Rényi Entropy and the Relationships between Rényi Capacities

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out so...

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Autores principales: Aishwarya, Gautam, Madiman, Mokshay
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7517019/
https://www.ncbi.nlm.nih.gov/pubmed/33286298
http://dx.doi.org/10.3390/e22050526
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author Aishwarya, Gautam
Madiman, Mokshay
author_facet Aishwarya, Gautam
Madiman, Mokshay
author_sort Aishwarya, Gautam
collection PubMed
description The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.
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spelling pubmed-75170192020-11-09 Conditional Rényi Entropy and the Relationships between Rényi Capacities Aishwarya, Gautam Madiman, Mokshay Entropy (Basel) Article The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored. MDPI 2020-05-06 /pmc/articles/PMC7517019/ /pubmed/33286298 http://dx.doi.org/10.3390/e22050526 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
Aishwarya, Gautam
Madiman, Mokshay
Conditional Rényi Entropy and the Relationships between Rényi Capacities
title Conditional Rényi Entropy and the Relationships between Rényi Capacities
title_full Conditional Rényi Entropy and the Relationships between Rényi Capacities
title_fullStr Conditional Rényi Entropy and the Relationships between Rényi Capacities
title_full_unstemmed Conditional Rényi Entropy and the Relationships between Rényi Capacities
title_short Conditional Rényi Entropy and the Relationships between Rényi Capacities
title_sort conditional rényi entropy and the relationships between rényi capacities
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7517019/
https://www.ncbi.nlm.nih.gov/pubmed/33286298
http://dx.doi.org/10.3390/e22050526
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