On the \(f\)-divergence for discrete non-additive measures
type: Item
instance of: scholarly article
title: On the \(f\)-divergence for discrete non-additive measures
zbMATH Open document ID: 1460.28012
author: Yasuo Narukawa
author: Michio Sugeno
author: Vicenç Torra
published in: Information Sciences
publication date: 2021-03-18T00:00:00Z
review text: Distances of probability measures, including f-divergences, Hellinger distance, Kullback-Leibler divergence, etc., play an important role in information theory and statistics. In several cases, the connection between these distances and Radon-Nikodym derivatives is exploited. The authors' aim in this paper is to introduce related distances considering monotone measures, hence replacing the sigma-additivity of classical measures by monotonicity. However, then the existence of a Radon-Nikodym derivative can be guaranteed only under quite restrictive constraints. These constraints (considering the discrete case only) are discussed. Also, when considering monotone measures, the Lebesgue integral cannot be exploited, in general, and therefore the integration in this paper is realized by means of the Choquet integral (observe that for sigma-additive measures, Lebesgue and Choquet integrals coincide). Restricting their considerations on a fixed finite space X, the authors have introduced and discussed f-divergence, Moebius transform-based f-divergence and Hellinger distance for monotone measures (called non-additive measures in this paper). Note that in some cases, e.g. in Definition 29, one can consider only belief functions as the considered monotone measures.
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 7325029
zbMATH Keywords: Choquet integral
zbMATH Keywords: f-divergence
zbMATH Keywords: Hellinger distance
zbMATH Keywords: Moebius transform
zbMATH Keywords: non-additive measure
zbMATH Keywords: Radon-Nikodym derivative
MaRDI profile type: Publication
full work available at URL: j.ins.2019.09.033
OpenAlex ID: W2974347212
cites work: A modified Kullback-Leibler divergence for non-additive measures based on Choquet integral
cites work: Q4788805
cites work: Q4821061
cites work: Q3686615
cites work: Conditional expectation for monotone measures, the discrete case
cites work: A generalization of \(f\)-divergence measure to convex functions defined on linear spaces
cites work: Cooperative Game as Non-Additive Measure
cites work: Additive representations of non-additive measures and the Choquet integral
cites work: Q3639652
cites work: Q4788833
cites work: A Radon-Nikodym theorem for capacities.
cites work: Theoretical Statistics
cites work: Integrals based on monotone set functions
cites work: Q4292505
cites work: An Introduction to Random Sets
cites work: Q4859898
cites work: A SUPER RADON-NIKODYM DERIVATIVE FOR ALMOST SUBADDITIVE SET FUNCTIONS
cites work: Q4172257
cites work: A note on derivatives of functions with respect to fuzzy measures
cites work: Entropy for non-additive measures in continuous domains
cites work: On the \(f\)-divergence for non-additive measures
DOI: 10.1016/J.INS.2019.09.033
description: scientific article; zbMATH DE number 7325029