Towards a generalization of information theory for hierarchical partitions.,Physical Review E

当前位置： X-MOL 学术 › Phys. Rev. E › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Towards a generalization of information theory for hierarchical partitions.
Physical Review E ( IF 2.2 ) Pub Date : 2020-06-30 , DOI: 10.1103/physreve.101.062148
Juan Ignacio Perotti _{1,

2} , Nahuel Almeira _{1,

2} , Fabio Saracco ₃

Affiliation

Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this phenomenon, we introduce a generalization of information theory that works with hierarchical partitions. We begin revisiting the recently introduced hierarchical mutual information (HMI), and show that it can be written as a level by level summation of classical conditional mutual information terms. Then, we prove that the HMI is bounded from above by the corresponding hierarchical joint entropy. In this way, in analogy to the classical case, we derive hierarchical generalizations of many other classical information-theoretic quantities. In particular, we prove that, as opposed to its classical counterpart, the hierarchical generalization of the variation of information is not a metric distance, but it admits a transformation into one. Moreover, focusing on potential applications of the existing developments of the theory, we show how to adjust by chance the HMI. We also corroborate and analyze all the presented theoretical results with exhaustive numerical computations, and include an illustrative application example of the introduced formalism. Finally, we mention some open problems that should be eventually addressed for the proposed generalization of information theory to reach maturity.

中文翻译：

迈向信息理论的层次划分。

复杂的系统通常表现出覆盖广泛物理范围的多个组织级别，因此对它们的结构和功能的层次分解进行研究通常很方便。为了更好地理解这种现象，我们引入了一种信息理论的概括，该理论适用于分层分区。我们开始回顾最近引入的分层互信息（HMI），并表明可以将其写成经典条件互信息项的逐级求和。然后，我们证明HMI从上方被相应的层次联合熵限制。这样，类似于经典案例，我们得出了许多其他经典信息理论量的层次概括。特别是，我们证明，与经典作品相比，信息变化的层次化概括不是度量距离，但它允许一种转换。此外，着重于该理论的现有发展的潜在应用，我们展示了如何偶然地调整HMI。我们还通过详尽的数值计算来证实和分析所有提出的理论结果，并包括所介绍形式主义的说明性应用示例。最后，我们提到了一些未解决的问题，这些问题最终应该解决以提出的信息理论泛化来达到成熟。我们还通过详尽的数值计算来证实和分析所有提出的理论结果，并包括所介绍形式主义的说明性应用示例。最后，我们提到了一些未解决的问题，这些问题最终应运用于提议的信息理论泛化以达到成熟。我们还通过详尽的数值计算来证实和分析所有提出的理论结果，并包括所介绍形式主义的说明性应用示例。最后，我们提到了一些未解决的问题，这些问题最终应该解决以提出的信息理论泛化来达到成熟。

更新日期：2020-06-30

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文本刊介绍/投稿指南11