Basic inequalities for weighted entropies
Information Theory
2016-01-15 v2 math.IT
Probability
Abstract
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of the weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cram\'{e}r-Rao inequalities involving the weighted Fisher information matrix.
Keywords
Cite
@article{arxiv.1510.02184,
title = {Basic inequalities for weighted entropies},
author = {Yuri Suhov and Izabella Stuhl and Salimeh Yasaei Sekeh and Mark Kelbert},
journal= {arXiv preprint arXiv:1510.02184},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1409.4102