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On weighted entropy of type ( α , β ) and its generalizations

Gur Dial, Inder Jeet Taneja (1981)

Aplikace matematiky

Belis and Guiasu studied a generalization of Shannon entropy as weighted or useful entropy. In this paper, the weighted entropy of type ( α , β ) is defined and characterized and some if its properties are studied. Further generalizations involving more parameters of weighted entropy are also specified.

Optimality conditions for maximizers of the information divergence from an exponential family

František Matúš (2007)

Kybernetika

The information divergence of a probability measure P from an exponential family over a finite set is defined as infimum of the divergences of P from Q subject to Q . All directional derivatives of the divergence from are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from are presented, including new ones when P  is not projectable to .

Optimally approximating exponential families

Johannes Rauh (2013)

Kybernetika

This article studies exponential families on finite sets such that the information divergence D ( P ) of an arbitrary probability distribution from is bounded by some constant D > 0 . A particular class of low-dimensional exponential families that have low values of D can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. The case where D = log ( 2 ) is studied in detail. This case is special, because if D < log ( 2 ) , then contains all probability...

Properties of unique information

Johannes Rauh, Maik Schünemann, Jürgen Jost (2021)

Kybernetika

We study the unique information function U I ( T : X Y ) defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of U I . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of T , X and Y . Our results are based on a reformulation of the first order conditions...

Refinement of the Jensen integral inequality

Silvestru Sever Dragomir, Muhammad Adil Khan, Addisalem Abathun (2016)

Open Mathematics

In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.

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