Inferring causal networks of dynamical systems through transient dynamics and perturbation
Abstract
Inferring causal relations from time series measurements is an illposed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between possible underlying causal networks by perturbing the network, where the forcings are either targeted or applied at random. The resulting transient dynamics provide the critical information necessary to infer causality. Two methods are shown to provide accurate causal reconstructions: Granger causality (GC) with perturbations, and our proposed perturbation cascade inference (PCI). Perturbed GC is capable of inferring smaller networks under low coupling strength regimes. Our proposed PCI method demonstrated consistently strong performance in inferring causal relations for small (25 node) and large (1020 node) networks, with both linear and nonlinear dynamics. Thus, the ability to apply a large and diverse set of perturbations to the network is critical for successfully and accurately determining causal relations and disambiguating between various viable networks.
 Publication:

Physical Review E
 Pub Date:
 October 2020
 DOI:
 10.1103/PhysRevE.102.042309
 arXiv:
 arXiv:2006.13154
 Bibcode:
 2020PhRvE.102d2309S
 Keywords:

 Mathematics  Dynamical Systems;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Statistics  Applications;
 37M10;
 62D20;
 62M10
 EPrint:
 11 pages, 9 figures