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Abstract：
Information is often described as a reduction of uncertainty associated with a restriction of possible choices. Despite appearing in Hartley\'s foundational work on information theory, there is a surprising lack of a formal treatment of this interpretation in terms of exclusions. This paper addresses the gap by providing an explicit characterisation of information in terms of probability mass exclusions. It then demonstrates that different exclusions can yield the same amount of information and discusses the insight this provides about how information is shared amongst random variables-lack of progress in this area is a key barrier preventing us from understanding how information is distributed in complex systems. The paper closes by deriving a decomposition of the mutual information which can distinguish between differing exclusions; this provides surprising insight into the nature of directed information.
摘要：
信息通常被描述为与可能选择的限制相关的不确定性的减少。尽管出现在哈特利的信息论基础工作中，令人惊讶的是，在排除方面缺乏对这种解释的正式处理。本文通过在概率质量排除方面提供明确的信息特征来解决这一差距。然后，它证明了不同的排除可以产生相同数量的信息，并讨论了这提供的关于信息如何在随机变量之间共享的见解-在这一领域缺乏进展是阻止我们理解信息如何在复杂系统中分布的关键障碍。本文通过得出可以区分不同排除的互信息的分解来结束；这提供了对定向信息性质的惊人见解。
