Reconstructing Networks with Unknown and Heterogeneous Errors

The vast majority of network data sets contain errors and omissions, although this fact is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network-reconstruction approaches based on Bayesian inference. These approaches, however, rely on assumptions of uniform error rates and on direct estimations of the existence of each edge via repeated measurements, something that is currently unavailable for the majority of network data. Here, we develop a Bayesian reconstruction approach that lifts these limitations by allowing for not only heterogeneous errors, but also for single edge measurements without direct error estimates. Our approach works by coupling the inference approach with structured generative network models, which enable the correlations between edges to be used as reliable uncertainty estimates. Although our approach is general, we focus on the stochastic block model as the basic generative process, from which efficient nonparametric inference can be performed and yields a principled method to infer hierarchical community structure from noisy data. We demonstrate the efficacy of our approach with a variety of empirical and artificial networks.