布尔函数的部分信息分解：傅立叶分析的观点
Partial Information Decomposition of Boolean Functions: a Fourier Analysis perspective
摘要：
部分信息分解（PID）将一组源关于目标变量的信息划分为协同的、唯一的和冗余的贡献。这种信息理论的工具，最近引起了人们的注意，由于其潜在的多变量系统中的信息处理的特点。然而，PID框架仍然缺乏对其信息组件的可靠和直观的解释。为了提高对PID组件的理解，我们在这里重点介绍布尔门，这是一种研究较多的源-目标机制。布尔门已被广泛的特点，通过傅立叶分析的系数已涉及到有趣的属性的功能，定义的门。在本文中，我们建立布尔门机构的PID组件和傅立叶系数之间的关系。
英文摘要：
Partial information decomposition (PID) partitions the information that a set of sources has about a target variable into synergistic, unique, and redundant contributions. This information-theoretic tool has recently attracted attention due to its potential to characterize the information processing in multivariate systems. However, the PID framework still lacks a solid and intuitive interpretation of its information components. In the aim to improve the understanding of PID components, we focus here on Boolean gates, a much-studied type of source-target mechanisms. Boolean gates have been extensively characterised via Fourier analysis which coefficients have been related to interesting properties of the functions defining the gates. In this paper, we establish for Boolean gates mechanisms a relation between their PID components and Fourier coefficients.
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