Granger causality has been widely used in various application domains to capture lead-lag relationships amongst the components of complex dynamical systems, and the focus in extant literature has been on a single dynamical system. In certain applications in macroeconomics and neuroscience, one has access to data from a collection of related such systems, wherein the modeling task of interest is to extract the shared common structure that is embedded across them, as well as to identify the idiosyncrasies within individual ones. This paper introduces a Variational Autoencoder (VAE) based framework that jointly learns Granger-causal relationships amongst components in a collection of related-yet-heterogeneous dynamical systems, and handles the aforementioned task in a principled way. The performance of the proposed framework is evaluated on several synthetic data settings and benchmarked against existing approaches designed for individual system learning. The method is further illustrated on a real dataset involving time series data from a neurophysiological experiment and produces interpretable results.

翻译：格兰杰因果关系被广泛用于捕捉复杂动态系统组分间的超前滞后关系，现有文献主要聚焦于单一动态系统。在宏观经济学与神经科学等特定应用中，研究者能够获取来自一组相关系统的数据，其建模任务既需提取跨系统的共享共性结构，又要识别各系统的特有异质性。本文提出一种基于变分自编码器（VAE）的框架，能够联合学习一组相关但异质动态系统中组分间的格兰杰因果关系，并以原理性方式处理上述任务。在多种合成数据场景下评估该框架性能，并与专为单一系统学习设计的现有方法进行基准对比。通过神经生理实验时间序列数据的真实应用案例，进一步验证了该方法可产生可解释的结果。