多元信息含量的广义测度
Generalised Measures of Multivariate Information Content
摘要：
一对随机变量的熵通常用维恩图来描述。然而，由于多元互信息可能是负的，因此这种表示可能会产生误导。本文提出了新的措施，可以准确地描述使用维恩图的任意数量的随机变量的多元信息含量。这些措施补充了现有的措施，多元互信息，并通过考虑信息共享的代数结构。结果表明，不同的方式，其中一组边缘观察员可以分享他们的信息与非观察第三方对应的元素的自由分配格。然后，通过结合联合和共享信息内容的代数结构，随后独立地导出来自部分信息分解的冗余格。
英文摘要：
The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a non-observing third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
