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Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

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Network transfer entropy and metric space for causality inference.

Christopher R S Banerji¹, Simone Severini, Andrew E Teschendorff

¹Department of Computer Science, University College London, London WC1E 6BT, United Kingdom. christopher.banerji.11@ucl.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 18, 2013

Summary

This study introduces a new network transfer entropy measure to quantify directed information flow and causal relationships in weighted networks. The method uses Jensen Shannon divergence to analyze network dynamics and their convergence.

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Area of Science:

Network Science
Information Theory
Complex Systems Analysis

Background:

Quantifying directed information transfer in complex networks is crucial for understanding system dynamics.
Existing methods may not fully capture causal relationships or handle weighted networks effectively.

Purpose of the Study:

To develop a novel measure for quantifying directed information transfer in weighted networks.
To establish a method for distinguishing and quantifying causal relationships between network elements.
To theoretically extend the framework using Jensen Shannon Divergence for metric space analysis.

Main Methods:

Derivation of a network transfer entropy measure based on a probabilistic model of network traffic.
Utilizing Jensen Shannon divergence to express informational distance between network dynamics.
Application to synthetic networks and a biological signaling network.

Main Results:

The developed measure successfully quantifies directed information transfer over specified path lengths.
Causal relationships between network elements were distinguished and quantified in tested networks.
A theoretical extension demonstrated that Jensen Shannon Divergence induces a metric on network dynamics.

Conclusions:

The network transfer entropy measure provides a robust tool for analyzing directed information flow and causality in weighted networks.
The theoretical framework offers a metric space for network dynamics, enabling convergence analysis.
This approach has implications for understanding complex systems, including biological signaling networks.