The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §

Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi and guessing entropies with respect to either error probability (yielding reverse-Fano and Fano inequalities) or total variation distance to the uniform (yielding reverse-Pinsker and...

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Autor principal: Rioul, Olivier
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10377982/
https://www.ncbi.nlm.nih.gov/pubmed/37509924
http://dx.doi.org/10.3390/e25070978
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author Rioul, Olivier
author_facet Rioul, Olivier
author_sort Rioul, Olivier
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description Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi and guessing entropies with respect to either error probability (yielding reverse-Fano and Fano inequalities) or total variation distance to the uniform (yielding reverse-Pinsker and Pinsker inequalities). This gives a general picture of how the notion of randomness can be measured in many areas of computer science.
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spelling pubmed-103779822023-07-29 The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities § Rioul, Olivier Entropy (Basel) Article Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi and guessing entropies with respect to either error probability (yielding reverse-Fano and Fano inequalities) or total variation distance to the uniform (yielding reverse-Pinsker and Pinsker inequalities). This gives a general picture of how the notion of randomness can be measured in many areas of computer science. MDPI 2023-06-25 /pmc/articles/PMC10377982/ /pubmed/37509924 http://dx.doi.org/10.3390/e25070978 Text en © 2023 by the author. https://creativecommons.org/licenses/by/4.0/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 (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Rioul, Olivier
The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §
title The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §
title_full The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §
title_fullStr The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §
title_full_unstemmed The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §
title_short The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities §
title_sort interplay between error, total variation, alpha-entropy and guessing: fano and pinsker direct and reverse inequalities §
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10377982/
https://www.ncbi.nlm.nih.gov/pubmed/37509924
http://dx.doi.org/10.3390/e25070978
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