Pairwise Network Information and Nonlinear Correlations

TL;DR

This paper introduces a novel entropy maximization approach using mutual information to efficiently determine pairwise interactions in complex networks, demonstrated on oscillator and brain networks.

Contribution

It proposes a new entropy maximization scheme based on conditioning on entropies and mutual information, improving over linear approximation methods.

Findings

Method outperforms linear approximation approaches.

Effective in oscillator and human brain network examples.

Reduces computational cost for network inference.

Abstract

Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated, or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples.