Network transfer entropy and metric space for causality inference

Christopher R. S. Banerji, Simone Severini, and Andrew E. Teschendorff
Phys. Rev. E 87, 052814 – Published 31 May 2013
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Abstract

A measure is derived to quantify directed information transfer between pairs of vertices in a weighted network, over paths of a specified maximal length. Our approach employs a general, probabilistic model of network traffic, from which the informational distance between dynamics on two weighted networks can be naturally expressed as a Jensen Shannon divergence. Our network transfer entropy measure is shown to be able to distinguish and quantify causal relationships between network elements, in applications to simple synthetic networks and a biological signaling network. We conclude with a theoretical extension of our framework, in which the square root of the Jensen Shannon Divergence induces a metric on the space of dynamics on weighted networks. We prove a convergence criterion, demonstrating that a form of convergence in the structure of weighted networks in a family of matrix metric spaces implies convergence of their dynamics with respect to the square root Jensen Shannon divergence metric.

  • Received 3 March 2013

DOI:https://doi.org/10.1103/PhysRevE.87.052814

©2013 American Physical Society

Authors & Affiliations

Christopher R. S. Banerji1,2,3,*, Simone Severini1,4, and Andrew E. Teschendorff3

  • 1Department of Computer Science, University College London, London WC1E 6BT, United Kingdom
  • 2Centre of Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, London WC1E 6BT, United Kingdom
  • 3Statistical Cancer Genomics, Paul O’Gorman Building, UCL Cancer Institute, University College London, London WC1E 6BT, United Kingdom
  • 4Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom

  • *christopher.banerji.11@ucl.ac.uk

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Issue

Vol. 87, Iss. 5 — May 2013

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