  We present a scalable nonparametric Bayesian method to perform network
reconstruction from observed functional behavior that at the same time infers
the communities present in the network. We show that the joint reconstruction
with community detection has a synergistic effect, where the edge correlations
used to inform the existence of communities are also inherently used to improve
the accuracy of the reconstruction which, in turn, can better inform the
uncovering of communities. We illustrate the use of our method with
observations arising from epidemic models and the Ising model, both on
synthetic and empirical networks, as well as on data containing only functional
information.
