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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Bibliographic Details
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/
Description
Summary: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.
ISSN:1099-4300

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