A utility-based approach to some information measures
type: Item
instance of: scholarly article
title: A utility-based approach to some information measures
zbMATH Open document ID: 1135.94315
author: Craig Friedman
author: Jinggang Huang
author: Sven Sandow
published in: Entropy
publication date: 2008-05-22T00:00:00Z
review text: Summary: We review a decision theoretic, i.e., utility-based, motivation for entropy and Kullback-Leibler relative entropy, the natural generalizations that follow, and various properties of these generalized quantities. We then consider these generalized quantities in an easily interpreted special case. We show that the resulting quantities, share many of the properties of entropy and relative entropy, such as the data processing inequality and the second law of thermodynamics. We formulate an important statistical learning problem -- probability estimation -- in terms of a generalized relative entropy. The solution of this problem reflects general risk preferences via the utility function; moreover, the solution is optimal in a sense of robust absolute performance.
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 62B10
zbMATH DE Number: 5278292
zbMATH Keywords: generalized entropy
zbMATH Keywords: generalized Kullback-Leibler relative entropy
zbMATH Keywords: decision theory
zbMATH Keywords: expected utility
zbMATH Keywords: horse race
zbMATH Keywords: Tsallis entropy
zbMATH Keywords: statistical learning
zbMATH Keywords: probability estimation
zbMATH Keywords: risk neutral pricing measure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e9010001
OpenAlex ID: W2171872837
DOI: 10.3390/E9010001
description: scientific article; zbMATH DE number 5278292