Basic inequalities for weighted entropies

Iouri M. Soukhov, Izabella Stuhl, Salimeh Yasaei Sekeh, Mark Kelbert

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cramér-Rao inequalities involving the weighted Fisher information matrix.

Original languageEnglish (US)
Pages (from-to)817-848
Number of pages32
JournalAequationes Mathematicae
Volume90
Issue number4
DOIs
StatePublished - Aug 1 2016

Fingerprint

Entropy
Weight Function
Hadamard's Inequality
Weighted Inequalities
Fisher Information Matrix
Positive definite matrix
Shannon Entropy
Fisher information matrix
Determinant
Fans
Dependent
Concepts
Context
Standards

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Soukhov, Iouri M. ; Stuhl, Izabella ; Yasaei Sekeh, Salimeh ; Kelbert, Mark. / Basic inequalities for weighted entropies. In: Aequationes Mathematicae. 2016 ; Vol. 90, No. 4. pp. 817-848.
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Basic inequalities for weighted entropies. / Soukhov, Iouri M.; Stuhl, Izabella; Yasaei Sekeh, Salimeh; Kelbert, Mark.

In: Aequationes Mathematicae, Vol. 90, No. 4, 01.08.2016, p. 817-848.

Research output: Contribution to journalArticle

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