The f -Divergence and Coupling of Probability Distributions

IF 0.5 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
V. V. Prelov
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引用次数: 1

Abstract

We consider the problem of finding the minimum and maximum values of f-divergence for discrete probability distributions P and Q provided that one of these distributions and the value of their coupling are given. An explicit formula for the minimum value of the f-divergence under the above conditions is obtained, as well as a precise expression for its maximum value. This precise expression is not explicit in the general case, but in many special cases it allows us to write out both explicit formulas and simple upper bounds, which are sometimes optimal. Similar explicit formulas and upper bounds are also obtained for the Kullback–Leibler and χ2 divergences, which are the most important cases of the f-divergence.

概率分布的f -散度与耦合
考虑离散概率分布P和Q的f散度的最小值和最大值问题,条件是给定其中一个分布及其耦合值。得到了上述条件下f-散度最小值的显式表达式,以及f-散度最大值的精确表达式。这个精确的表达式在一般情况下并不显式,但在许多特殊情况下,它允许我们写出显式公式和简单的上界,这有时是最优的。对于f-散度最重要的情况Kullback-Leibler散度和χ2散度,也得到了类似的显式公式和上界。
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来源期刊
Problems of Information Transmission
Problems of Information Transmission 工程技术-计算机:理论方法
CiteScore
2.00
自引率
25.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: Problems of Information Transmission is of interest to researcher in all fields concerned with the research and development of communication systems. This quarterly journal features coverage of statistical information theory; coding theory and techniques; noisy channels; error detection and correction; signal detection, extraction, and analysis; analysis of communication networks; optimal processing and routing; the theory of random processes; and bionics.
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