Maximally informative pairwise interactions in networks

TL;DR

This paper develops a method to optimize input-to-network mappings for maximal information transfer using pairwise interactions modeled by the Ising model, revealing how input distribution influences network interactions.

Contribution

It introduces a novel approach to determine optimal pairwise interactions in networks for maximal information transfer, including linear equations for Ising model parameters and geometric applicability criteria.

Findings

Optimal interactions are zero for Gaussian and uniform inputs.

Non-zero interactions increase with natural-like input distributions.

Interactions grow stronger with increased response noise.

Abstract

Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings between input signals and network states that allow the network to convey the maximal information about input signals drawn from a given distribution. This mapping also produces a set of linear equations for calculating the optimal Ising model coupling constants, as well as geometric properties that indicate the applicability of the pairwise Ising model. We show that the optimal pairwise interactions are on average zero for Gaussian and uniformly distributed inputs, whereas they are non-zero for inputs approximating those in natural environments. These non-zero network interactions are predicted to increase in strength as the noise in the response functions of each network node increases. This approach also suggests ways for how interactions with unmeasured parts of the network can be inferred from the parameters of response functions for the measured network nodes.