A Control Theoretic Look at Granger Causality: Extending Topology Reconstruction to Networks With Direct Feedthroughs
A Control Theoretic Look at Granger Causality: Extending Topology Reconstruction to Networks With Direct Feedthroughs
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DOI：
10.1109/tac.2020.2989261
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发表时间：
2021-02
影响因子：
6.8
通讯作者：
Mihaela Dimovska;D. Materassi
中科院分区：
文献类型：
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作者：
Mihaela Dimovska;D. Materassi
从观测数据重建动态系统网络的因果结构是许多科学领域的重要问题。解决这一问题的最早和最突出的方法之一是格兰杰因果关系。已经证明，在具有线性动态和严格因果传递函数的网络中，格兰杰因果性一致地重构网络的底层图。另一方面，允许存在直接馈通的技术通常假设在网络的动态中没有反馈环路。在这篇文章中，我们发展了Granger因果关系的一个扩展，它为即使在存在直接反馈和反馈回路的情况下重建网络拓扑提供了理论保证。唯一需要的假设是一个相对温和的适定性条件，称为递归性，其中每个反馈回路中至少需要存在一个严格的因果传递函数。将该技术与其他最先进的方法在一个基准测试示例上进行了比较，该基准示例专门设计为包括几个具有挑战性的动态配置。
Reconstructing the causal structure of a network of dynamic systems from observational data is an important problem in many areas of science. One of the earliest and most prominent approaches to this problem is Granger causality. It has been shown that in a network with linear dynamics and strictly causal transfer functions, Granger causality consistently reconstructs the underlying graph of the network. On the other hand, techniques that allow for the presence of direct feedthroughs usually assume there are no feedback loops in the dynamics of the network. In this article, we develop an extension of Granger causality that provides theoretical guarantees for the reconstruction of a network topology even in the presence of direct feedthroughs and feedback loops. The only required assumption is a relatively mild condition of well-posedness named recursiveness, where at least one strictly causal transfer function needs to be present in every feedback loop. The technique is compared with other state-of-the-art methods on a benchmark example specifically designed to include several dynamic configurations that are challenging to reconstruct.