vix.ing · top · new · best · stats · spec

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

2020/12/07 by Milan Studený, Milan Studeny · 1 citation
Computer Science · Decision Sciences · Mathematics · #Applied mathematics #Bayesian Modeling and Causal Inference #Calculus (dental) #Chain rule (probability) #Conditional entropy #Conditional expectation #Conditional independence #Conditional mutual information #Conditional probability #Discrete mathematics #Econometrics #Entropy (arrow of time) #Fuzzy Systems and Optimization #Independence (probability theory) #Inequality #Mathematical analysis #Mathematical economics #Mathematical proof #Mathematics #Multi-Criteria Decision Making #Principle of maximum entropy #Probability mass function #Random variable #Regular conditional probability #Rough Sets and Fuzzy Logic #Statistics #cs.AI #cs.IT #math.CO #math.IT #msc:52B40 #msc:68T37 #msc:94A17

paper · pdf · doi:10.1109/tit.2021.3104250

published as IEEE Transactions on Information Theory, vol. 67, no. 11, November 2021, pp. 7030 - 7049

openalex publication_date 2020/12/07 · openalex created_date 2021/08/30 · arxiv created 2022/03/14 · arxiv updated 2022/03/16 · openalex updated_date 2026/08/05

Abstract

The paper deals with conditional 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.

Citations

Cited by