  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.
