Network Representation of Higher-Order Interactions Based on Information Dynamics
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基于信息动力学的高阶交互网络表示
- 研究问题
- 传统成对网络可能遗漏三个及以上动态过程共享的信息，如何在整体、连接和节点层面紧凑表示高阶交互？
- 方法与思路
- 作者结合动态 O-information、局部对应量及梯度刻画多层次交互，并用向量回归和统计验证实现线性版本。
- 材料陈述的贡献
- 摘要提出将高阶交互整合到传统网络表示的框架，给出形式化定义、线性实现，并展示模拟及网络生理学应用。
- 阅读关注点
- 应核对信息量及梯度的解释、线性实现的适用条件，以及统计验证如何区分高阶依赖与成对关联。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要不足以判断高阶信息指标能否解释为因果作用。
原文摘要
Many complex systems in science and engineering are modeled as networks whose nodes and links depict the temporal evolution of each system unit and the dynamic interaction between pairs of units, which are assessed respectively using measures of auto- and cross-correlation or variants thereof. However, a growing body of work is documenting that this standard network representation can neglect potentially crucial information shared by three or more dynamic processes in the form of higher-order interactions (HOIs). While several measures, mostly derived from information theory, are available to assess HOIs in network systems mapped by multivariate time series, none of them is able to provide a compact and detailed representation of higher-order interdependencies. In this work, we fill this gap by introducing a framework for the assessment of HOIs in dynamic network systems at different levels of resolution. The framework is grounded on the dynamic implementation of the O-information, a new measure assessing HOIs in dynamic networks, which is here used together with its local counterpart and its gradient to quantify HOIs respectively for the network as a whole, for each link, and for each node. The integration of these measures into the conventional network representation results in a tool for the representation of HOIs as networks, which is defined formally using measures of information dynamics, implemented in its linear version by using vector regression models and statistical validation techniques, illustrated in simulated network systems, and finally applied to an illustrative example in the field of network physiology.