A Control Theoretic Look at Granger Causality: Extending Topology Reconstruction to Networks with Direct Feedthroughs

Mihaela Dimovska, Donatello Materassi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article number9072648
Pages (from-to)699-713
Number of pages15
JournalIEEE Transactions on Automatic Control
Volume66
Issue number2
DOIs
StatePublished - Feb 2021

Bibliographical note

Funding Information:
Manuscript received September 7, 2019; revised January 27, 2020; accepted April 8, 2020. Date of publication April 20, 2020; date of current version January 28, 2021. This work was supported by NSF CAREER Award 1553504 and NSF SaTC 1816703. Recommended by Associate Editor G. Gu. (Corresponding author: Mihaela Dimovska.) The authors are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: dimov003@umn.edu; mater013@umn.edu).

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Learning (artificial intelligence)
  • stochastic processes
  • system identification
  • time series analysis

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