منابع مشابه
Sharp Inequalities for $f$-divergences
f -divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an f -dive...
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We study conditions on f under which an f -divergence Df will satisfy Df ≥ cfV 2 or Df ≥ c2,fV +c4,fV , where V denotes variational distance and the coefficients cf , c2,f and c4,f are best possible. As a consequence, we obtain lower bounds in terms of V for many well known distance and divergence measures. For instance, let D(α)(P,Q) = [α(α− 1)][ ∫ qp dμ− 1] and Iα(P,Q) = (α−1)−1 log[ ∫ pq dμ]...
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X iv :1 10 4. 56 03 v2 [ co nd -m at .s ta tm ec h] 1 8 O ct 2 01 1 Mathematical inequalities for some divergences S. Furuichiand F.-C. Mitroi Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan University of Craiova, Department of Mathematics, Street A. I. Cuza 13, Craiova, RO-2005...
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We study conditions on f under which an f -divergence Df will satisfy Df ≥ cfV 2 or Df ≥ c2,fV 2 + c4,fV 4, where V denotes variational distance and the coefficients cf , c2,f and c4,f are best possible. As a consequence, we obtain lower bounds in terms of V for many well known distance and divergence measures. For instance, let D(α)(P,Q) = [α(α−1)]−1[∫ qαp1−α dμ−1] and Iα(P,Q) = (α−1)−1 log[ ∫...
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where μ is a nonnegative measure on [0,∞) such that the integral (2) converges for all x > 0. This means that a function f(x) is completely monotonic on (0,∞) if and only if it is a Laplace transform of the measure μ. The completely monotonic functions have applications in different branches of mathematical sciences. For example, they play some role in combinatorics, numerical and asymptotic an...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2014
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2013.2288674