Inference of time-varying networks through transfer entropy, the case of a Boolean network model

Maurizio Porfiri, Manuel Ruiz Marín

Research output: Contribution to journalArticle

Abstract

Inferring network topologies from the time series of individual units is of paramount importance in the study of biological and social networks. Despite considerable progress, our success in network inference is largely limited to static networks and autonomous node dynamics, which are often inadequate to describe complex systems. Here, we explore the possibility of reconstructing time-varying weighted topologies through the information-theoretic notion of transfer entropy. We focus on a Boolean network model in which the weight of the links and the spontaneous activity periodically vary in time. For slowly-varying dynamics, we establish closed-form expressions for the stationary periodic distribution and transfer entropy between each pair of nodes. Our results indicate that the instantaneous weight of each link is mapped into a corresponding transfer entropy value, thereby affording the possibility of pinpointing the dominant weights at each time. However, comparing transfer entropy readings at different times may provide erroneous estimates of the strength of the links in time, due to a counterintuitive modulation of the information flow by the non-autonomous dynamics. In fact, this time variation should be used to scale transfer entropy values toward the correct inference of the time evolution of the network weights. This study constitutes a necessary step toward a mathematically-principled use of transfer entropy to reconstruct time-varying networks.

Original languageEnglish (US)
Article number103123
JournalChaos
Volume28
Issue number10
DOIs
StatePublished - Oct 1 2018

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Time varying networks
Boolean Model
Boolean Networks
inference
Network Model
Time-varying
Entropy
entropy
Topology
Biological Networks
Information Flow
topology
Vertex of a graph
Network Topology
Social Networks
Instantaneous
Telecommunication links
information flow
Large scale systems
Time series

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Inference of time-varying networks through transfer entropy, the case of a Boolean network model. / Porfiri, Maurizio; Ruiz Marín, Manuel.

In: Chaos, Vol. 28, No. 10, 103123, 01.10.2018.

Research output: Contribution to journalArticle

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