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Sumset and Inverse Sumset Inequalities for Differential Entropy and Mutual Information
Shannon entropy differential entropy sumset bounds inequalities submodularity data processing mutual information
2012/6/19
The sumset and inverse sumset theories of Freiman, Pl\"{u}nnecke and Ruzsa, give bounds connecting the cardinality of the sumset $A+B=\{a+b\;;\;a\in A,\,b\in B\}$ of two discrete sets $A,B$, to the ca...
R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. Th...
Explicit Bounds for Entropy Concentration under Linear Constraints
maximum entropy concentration bounds linear constraints tolerances
2011/9/23
Abstract: Consider the construction of an object composed of $m$ parts by distributing $n$ units to those parts. For example, say we are assigning $n$ balls to $m$ boxes. Each assignment results in a ...
The entropy functional, the information path functional's essentials and their connections to Kolmogorov's entropy, complexity and physics
Additive functional Entropy Singularities Natural Border Problem Invariant
2011/8/31
Abstract: The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connect...