Non-linear Information Inequalities

Non-linear Information Inequalities

We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a...

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Main Authors: Terence Chan, Alex Grant
Format: Article
Language:English
Published: MDPI AG 2008-12-01
Series:Entropy
Subjects:
Entropy
entropy function
nonlinear information inequality
nonshannon type information inequality
Online Access:http://www.mdpi.com/1099-4300/10/4/765/
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spelling doaj-536c6c86801843e1a542b7ca0a3075042020-11-24T22:47:31ZengMDPI AGEntropy1099-43002008-12-0110476577510.3390/e10040765Non-linear Information InequalitiesTerence ChanAlex GrantWe construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities.http://www.mdpi.com/1099-4300/10/4/765/Entropyentropy functionnonlinear information inequalitynonshannon type information inequality
collection DOAJ
language English
format Article
sources DOAJ
author Terence Chan
Alex Grant
spellingShingle Terence Chan
Alex Grant
Non-linear Information Inequalities
Entropy
Entropy
entropy function
nonlinear information inequality
nonshannon type information inequality
author_facet Terence Chan
Alex Grant
author_sort Terence Chan
title Non-linear Information Inequalities
title_short Non-linear Information Inequalities
title_full Non-linear Information Inequalities
title_fullStr Non-linear Information Inequalities
title_full_unstemmed Non-linear Information Inequalities
title_sort non-linear information inequalities
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2008-12-01
description We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities.
topic Entropy
entropy function
nonlinear information inequality
nonshannon type information inequality
url http://www.mdpi.com/1099-4300/10/4/765/
work_keys_str_mv AT terencechan nonlinearinformationinequalities
AT alexgrant nonlinearinformationinequalities
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