信息分解的连续性和可加性

Johannes Rauh, P. Banerjee, E. Olbrich, Guido Montúfar, J. Jost
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引用次数: 2

摘要

信息分解量化了关于给定随机变量的香农信息如何分布在其他几个随机变量中。已经提出了这种分解应该满足的各种需求,从而导致不同的候选解决方案。然而,奇怪的是,只考虑了确定香农信息的两个原始要求,即单调性和规范化。另外两个重要的性质,连续性和可加性,没有被考虑。在这篇贡献中,我们关注两个有限变量$Y,Z$关于第三个有限变量$S$的互信息,并检查哪些分解满足这两个性质。它们大多满足连续性,但只有一个是连续和可加的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Continuity and Additivity Properties of Information Decompositions
Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been proposed that such a decomposition should satisfy, leading to different candidate solutions. Curiously, however, only two of the original requirements that determined the Shannon information have been considered, namely monotonicity and normalization. Two other important properties, continuity and additivity, have not been considered. In this contribution, we focus on the mutual information of two finite variables $Y,Z$ about a third finite variable $S$ and check which of the decompositions satisfy these two properties. While most of them satisfy continuity, only one of them is both continuous and additive.
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