Bootstrapping networks with latent space structure

Keith Levin, Liza Levina

Abstract: A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data presents a particular challenge, since one typically observes a single network rather than a sample. Here we propose two methods for obtaining bootstrap samples for networks drawn from latent space models. The first method generates bootstrap replicates of network statistics that can be represented as U-statistics in the latent positions, and avoids actually constructing new bootstrapped networks. Many network quantities can be represented as U-statistics, including average degree and subgraph counts, but other equally popular summaries, such as clustering coefficients, are not expressible as U-statistics. Our second bootstrapping method generates replicates of whole networks, and thus can be used for bootstrapping more general network functions. Under the assumption of a random dot product graph, a type of latent space network model, we show consistency of the proposed bootstrap methods. We give motivating examples throughout and demonstrate the effectiveness of our methods on both synthetic and real data and show that they improve upon prior methods.