Granger causality (GC), a popular statistical method for the inference of directional influences between time series measured from a complex network, is sensitive to high-order (non-pairwise) interactions which fundamentally shape the collective network dynamics. This work introduces Partial Decomposition of Granger Causality (PDGC), a tool eliciting redundant and synergistic causal interactions in the pattern of information flow between the subsystems of physiological networks. The tool exploits the framework of partial information decomposition to dissect the multivariate GC from a set of driver random processes to a target process into unique effects carried exclusively by each driver, redundant effects carried identically by more drivers, and synergistic effects carried jointly by some drivers but not by any of them individually. Computation is based on multivariate state-space models expanded in the frequency domain to assess PDGC both in specific bands of physiological interest and in the time domain after whole-band integration. The spectral PDGC was tested in physiological networks probed by measuring the variability series of arterial pressure, heart period, respiration and cerebral blood velocity in patients prone to neurally-mediated syncope compared to healthy controls. This application revealed unprecedented modes of physiological interaction, related to the sympathetic control of low-frequency cardiovascular and cerebrovascular oscillations, characterizing distinctive patterns of autonomic dysfunction. The extraction of high-order causality patterns from the spectral GC favors dissecting the mechanisms of causal influence underlying multivariate interactions among oscillatory processes in many data-driven applications of network science.

翻译：格兰杰因果性（GC）是一种用于推断复杂网络所测时间序列间方向性影响的流行统计方法，它对高阶（非成对）相互作用高度敏感，而这些相互作用从根本上塑造了集体网络动力学。本研究引入了格兰杰因果性偏分解（PDGC），这是一种能够揭示生理网络子系统间信息流模式中冗余与协同因果相互作用的工具。该工具利用偏信息分解框架，将一组驱动随机过程到目标过程的多变量GC分解为：由每个驱动过程单独承载的独特效应、由多个驱动过程相同地承载的冗余效应，以及由某些驱动过程联合承载但任何单个过程均无法单独承载的协同效应。计算基于在频域展开的多变量状态空间模型，以评估特定生理相关频带内的PDGC，以及在全频带积分后的时域PDGC。光谱PDGC在生理网络中进行了测试，通过测量易发生神经介导性晕厥患者与健康对照者的动脉压、心动周期、呼吸和脑血流速度的变异性序列来探测网络。此应用揭示了前所未有的生理相互作用模式，这些模式与低频心血管和脑血管振荡的交感神经控制相关，表征了自主神经功能障碍的独特模式。从光谱GC中提取高阶因果性模式，有助于在网络科学的许多数据驱动应用中解析振荡过程间多变量相互作用背后的因果影响机制。