Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities

0547016 - ÚTIA 2022 RIV US eng J - Journal Article
Studený, Milan
Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities.
IEEE Transactions on Information Theory. Roč. 67, č. 11 (2021), s. 7030-7049. ISSN 0018-9448. E-ISSN 1557-9654
R&D Projects: GA ČR(CZ) GA19-04579S
Institutional support: RVO:67985556
Keywords : entropy function * discrete random variables * conditional information inequalities * conditional independence * polymatroids
OECD category: Pure mathematics
Impact factor: 2.978, year: 2021
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2021/MTR/studeny-0547016-P.pdf https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9514618

The paper deals with linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid under conditional independence assumptions on the inducing random variables. We discuss five inequalities of this particular type, four of which has appeared earlier in the literature. Besides the proof of the new fifth inequality, simpler proofs of (some of) former inequalities are presented. These five information inequalities are used to characterize all conditional independence structures induced by four discrete random variables.
Permanent Link: http://hdl.handle.net/11104/0323438