Conditions for the existence of a generalization of Rényi divergence

Detalhes bibliográficos
Autor(a) principal: Vigelis, Rui Facundo
Data de Publicação: 2020
Outros Autores: Andrade, Luiza Helena Félix de, Cavalcante, Charles Casimiro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
Texto Completo: http://www.repositorio.ufc.br/handle/riufc/69734
Resumo: We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.
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spelling Conditions for the existence of a generalization of Rényi divergenceGeneralized divergenceRényi entropyInformation geometryExistence conditionsEntropia (Teoria da informação)We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.Physica A: Statistical Mechanics and its Applications2022-12-14T18:21:47Z2022-12-14T18:21:47Z2020info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCAVALCANTE, C. C.; ANDRADE, L. H. F.; VIGÉLIS, R. F. Conditions for the existence of a generalization of Rényi divergence. Physica A: Statistical Mechanics and its Applications, [s.l.], v. 558, 2020. DOI: https://doi.org/10.1016/j.physa.2020.1249530378-4371http://www.repositorio.ufc.br/handle/riufc/69734Vigelis, Rui FacundoAndrade, Luiza Helena Félix deCavalcante, Charles Casimiroengreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccess2022-12-16T13:22:44Zoai:repositorio.ufc.br:riufc/69734Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2024-09-11T18:46:02.679046Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.none.fl_str_mv Conditions for the existence of a generalization of Rényi divergence
title Conditions for the existence of a generalization of Rényi divergence
spellingShingle Conditions for the existence of a generalization of Rényi divergence
Vigelis, Rui Facundo
Generalized divergence
Rényi entropy
Information geometry
Existence conditions
Entropia (Teoria da informação)
title_short Conditions for the existence of a generalization of Rényi divergence
title_full Conditions for the existence of a generalization of Rényi divergence
title_fullStr Conditions for the existence of a generalization of Rényi divergence
title_full_unstemmed Conditions for the existence of a generalization of Rényi divergence
title_sort Conditions for the existence of a generalization of Rényi divergence
author Vigelis, Rui Facundo
author_facet Vigelis, Rui Facundo
Andrade, Luiza Helena Félix de
Cavalcante, Charles Casimiro
author_role author
author2 Andrade, Luiza Helena Félix de
Cavalcante, Charles Casimiro
author2_role author
author
dc.contributor.author.fl_str_mv Vigelis, Rui Facundo
Andrade, Luiza Helena Félix de
Cavalcante, Charles Casimiro
dc.subject.por.fl_str_mv Generalized divergence
Rényi entropy
Information geometry
Existence conditions
Entropia (Teoria da informação)
topic Generalized divergence
Rényi entropy
Information geometry
Existence conditions
Entropia (Teoria da informação)
description We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.
publishDate 2020
dc.date.none.fl_str_mv 2020
2022-12-14T18:21:47Z
2022-12-14T18:21:47Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv CAVALCANTE, C. C.; ANDRADE, L. H. F.; VIGÉLIS, R. F. Conditions for the existence of a generalization of Rényi divergence. Physica A: Statistical Mechanics and its Applications, [s.l.], v. 558, 2020. DOI: https://doi.org/10.1016/j.physa.2020.124953
0378-4371
http://www.repositorio.ufc.br/handle/riufc/69734
identifier_str_mv CAVALCANTE, C. C.; ANDRADE, L. H. F.; VIGÉLIS, R. F. Conditions for the existence of a generalization of Rényi divergence. Physica A: Statistical Mechanics and its Applications, [s.l.], v. 558, 2020. DOI: https://doi.org/10.1016/j.physa.2020.124953
0378-4371
url http://www.repositorio.ufc.br/handle/riufc/69734
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Physica A: Statistical Mechanics and its Applications
publisher.none.fl_str_mv Physica A: Statistical Mechanics and its Applications
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
repository.mail.fl_str_mv bu@ufc.br || repositorio@ufc.br
_version_ 1813028938164731904

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