title: Network transfer entropy and metric space for causality inference.
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.
authors.affiliation: Department of Computer Science, University College London, London WC1E 6BT, United Kingdom. christopher.banerji.11@ucl.ac.uk
authors.forename: Christopher R S
authors.initials: CR
authors.lastname: Banerji
authors.forename: Simone
authors.initials: S
authors.lastname: Severini
authors.forename: Andrew E
authors.initials: AE
authors.lastname: Teschendorff
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D055442:Metabolome / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D015398:Signal Transduction / Q000502:physiology*