Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation

TL;DR

This paper presents methods for inferring causal networks in dynamical systems by applying targeted or random perturbations and analyzing transient responses, improving accuracy in small and large networks with linear and nonlinear dynamics.

Contribution

It introduces a novel perturbation cascade inference (PCI) method and demonstrates its effectiveness alongside Granger causality with perturbations for causal network reconstruction.

Findings

Perturbed Granger causality works well for small networks with low coupling.

PCI method shows strong performance for both small and large networks.

Applying diverse perturbations is crucial for accurate causal inference.

Abstract

Inferring causal relations from time series measurements is an ill-posed 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 actuations 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 (2-5 node) and large (10-20 node) networks, with both linear and nonlinear dynamics. Thus the ability to apply a large and diverse set of perturbations/actuations to the network is critical for successfully and accurately determining causal relations and disambiguating between various viable networks.