Conditional Independence Structures over Four Discrete Random Variables Revisited: Conditional Ingleton Inequalities
نویسندگان
چکیده
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 center of interest: these under conditional independence assumptions on inducing We discuss five this particular type, four which has appeared earlier literature. Besides proof new fifth inequality, simpler proofs (some of) former presented. These used to characterize all structures
منابع مشابه
Testing Conditional Independence for Continuous Random Variables
A common statistical problem is the testing of independence of two (response) variables conditionally on a third (control) variable. In the first part of this paper, we extend Hoeffding’s concept of estimability of degree r to testability of degree r, and show that independence is testable of degree two, while conditional independence is not testable of any degree if the control variable is con...
متن کاملConditional Independences among Four Random Variables Ii
Numerous new properties of stochastic conditional independence are introduced. They are aimed, together with two surprisingly trivial examples, at a further reduction of the problem of probabilistic representability for four{element sets, i.e. of the problem which conditional independences within a system of four random variables can occur simultaneously. Proofs are based on fundamental propert...
متن کاملConditional Independences among Four Random Variables 2
The conditional independences within a system of four discrete random variables are studied simultaneously. The problem where independences can occur at the same time, called the problem of probabilistic representability, is attacked by an analysis of cones of polymatroids. New results on the cone of all polymatroids satisfying Ingleton inequalities imply a substantial reduction of the problem ...
متن کاملConditional Independences among Four Random Variables I
The conditional independences within a system of four discrete random variables are studied simultaneously. The problem where independences can occur at the same time, called the problem of probabilistic representability, is attacked by an analysis of cones of polymatroids. New results on the cone of all polymatroids satisfying Ingleton inequalities imply a substantial reduction of the problem ...
متن کاملOn Gaussian conditional independence structures
The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2021
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2021.3104250