论文标题
布尔函数的部分信息分解：傅立叶分析观点
Partial Information Decomposition of Boolean Functions: a Fourier Analysis perspective
论文作者
论文摘要
部分信息分解（PID）将一组源具有有关目标变量的信息分配给协同，独特和冗余的贡献。该信息理论工具最近引起了人们的关注，因为它有可能表征多元系统中的信息处理。但是，PID框架仍然缺乏对其信息组件的坚实而直观的解释。为了提高对PID组件的理解，我们将重点放在布尔门（Boolean Gates）上，布尔门（Boolean Gates）是一种众所周知的源目标机制。布尔门已经通过傅立叶分析进行了广泛的表征，这些系数与定义门的功能的有趣特性有关。在本文中，我们建立了布尔门机制的PID组件与傅立叶系数之间的关系。
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.
