Network Transfer Entropy and Metric Space for Causality Inference

TL;DR

This paper introduces a novel measure called network transfer entropy based on Jensen Shannon Divergence to quantify directed information transfer and causality in weighted networks, with applications to synthetic and biological networks.

Contribution

It develops a probabilistic framework for causality inference in networks and extends it to a metric space using the square root of JSD, including convergence properties.

Findings

The measure can distinguish causal relationships in networks.

Application to biological signaling networks demonstrates practical utility.

Theoretical proof of convergence in network dynamics using the metric.

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 (JSD). 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 signalling network. We conclude with a theoretical extension of our framework, in which the square root of the JSD 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 JSD metric.