Higher order optimal approximation of Csiszar's \(f\)-divergence
type: Item
instance of: scholarly article
title: Higher order optimal approximation of Csiszar's \(f\)-divergence
zbMATH Open document ID: 1071.60009
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-05-12T00:00:00Z
review text: Let \((X,\mathcal A,\lambda)\) be a measure space, \(\mu_1,\mu_2\) be probability measures on \((X,\mathcal A)\) absolutely continuous with respect to \(\lambda\), and it is assumed that \(p=d\mu_1/d\lambda\) and \(q=d\mu_2/d\lambda\) are such that \(0<a\leq p/q\leq b<\infty\). For a convex function \(f\), the quantity \[ \Gamma_f(\mu_1,\mu_2)=\int_Xq(x)f\left( \frac{p(x)}{q(x)}\right) \,d\lambda (x) \] is called the \(f\)-divergence (or Csiszár's distance) of \(\mu_1\) and \(\mu_2\) [\textit{I. Csiszár}, Stud. Sci. Math. Hung. 2, 299--318 (1967; Zbl 0157.25802)]. The author obtains several representation formulas for the \(f\)-divergence, which lead, under various assumptions, to precise estimates of \(\Gamma_f\).
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 28A33
zbMATH DE Number: 2167862
zbMATH Keywords: Csiszar's distance
author: George A. Anastassiou
MaRDI profile type: Publication
full work available at URL: j.na.2004.09.049
OpenAlex ID: W2028372284
cites work: Q4271953
cites work: Q4659345
cites work: Q3603133
cites work: Q5705616
cites work: Approximating Csiszár f-divergence by the use of Taylor's formula with integral remainder
cites work: Trapezoidal-type rules from an inequalities point of view
cites work: Q5737389
cites work: Q5539510
cites work: Q5529067
cites work: On Information and Sufficiency
cites work: Q3292859
DOI: 10.1016/J.NA.2004.09.049
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description: scientific article; zbMATH DE number 2167862