论文标题
信息分解的连续性和添加性属性
Continuity and Additivity Properties of Information Decompositions
论文作者
论文摘要
信息分解量化了有关给定随机变量的香农信息如何分布在其他几个随机变量之间。已经提出了各种要求，应满足这种分解，从而导致不同的候选解决方案。然而，奇怪的是，只有两个确定香农信息的原始要求，即单调性和归一化。尚未考虑另外两个重要的属性，即连续性和增强性。在此贡献中，我们专注于两个有限变量$ y，z $的共同信息，约为第三个有限变量$ s $，并检查哪些分解满足了这两个属性。尽管大多数人都满足连续性，但其中只有一个既连续又是添加剂。
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.
