Hierarchical Quantification of Synergy in Channels
Hierarchical Quantification of Synergy in Channels
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DOI：
10.3389/frobt.2015.00035
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发表时间：
2016-01-08
影响因子：
3.4
通讯作者：
Ay, Nihat
中科院分区：
文献类型：
--
作者：
Perrone, Paolo;Ay, Nihat
将渠道信息分解为不同阶次的协同效应是复杂系统理论中一个开放的、活跃的问题。大多数方法的问题是基于信息论，并提出了几种方式的输入和输出之间的互信息的分解，其中没有一个是普遍接受的。我们提出了一个新的观点。我们将多输入信道建模为马尔可夫核。我们可以将信道投影到一系列指数族上，这些指数族形成了一个分层结构。这是用信息几何的工具进行的，类似于Amari介绍的概率分布的投影。毕达哥拉斯关系自然导致输入和输出之间的互信息分解为项，项表示单节点信息、成对交互以及一般的n节点交互。本文介绍的协同措施，可以很容易地评估的迭代缩放算法，这是一个标准的信息几何过程。
The decomposition of channel information into synergies of different order is an open, active problem in the theory of complex systems. Most approaches to the problem are based on information theory and propose decompositions of mutual information between inputs and outputs in several ways, none of which is generally accepted yet. We propose a new point of view on the topic. We model a multi-input channel as a Markov kernel. We can project the channel onto a series of exponential families, which form a hierarchical structure. This is carried out with tools from information geometry in a way analogous to the projections of probability distributions introduced by Amari. A Pythagorean relation leads naturally to a decomposition of the mutual information between inputs and outputs into terms, which represent single node information, pairwise interactions, and in general n-node interactions. The synergy measures introduced in this paper can be easily evaluated by an iterative scaling algorithm, which is a standard procedure in information geometry.