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 check which of the decompositions satisfy these two properties. While most of them satisfy continuity, only one of them satisfies additivity.
翻译:信息分解可以量化香农关于某一随机变量的信息如何在其它几个随机变量之间分配; 提出了各种要求,要求这种分解应满足要求,导致不同的候选解决方案; 然而,奇怪的是,在确定香农信息的最初要求中,只考虑了两项要求,即单一性和正常化; 尚未考虑另外两项重要的属性、连续性和相加性; 在这项贡献中,我们检查哪些分解满足了这两个属性; 虽然其中多数满足了连续性,但只有一项满足了补充性。