Bootstrapping Networks with Latent Space Structure

TL;DR

This paper introduces two bootstrap methods for latent space network models, enabling reliable inference for network statistics and functions from a single observed network, with proven consistency under certain models.

Contribution

It proposes novel bootstrap techniques for latent space networks, including U-statistics-based and full network resampling methods, with theoretical validation.

Findings

Methods are consistent under the random dot product graph model.

Effective on synthetic data for network statistics and functions.

Allows inference from a single observed network.

Abstract

A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only 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. The second method generates bootstrap replicates of whole networks, and thus can be used for bootstrapping any network function. Commonly studied network quantities that can be represented as U-statistics include many popular summaries, such as average degree and subgraph counts, but other equally popular summaries, such as the clustering coefficient, are not expressible as U-statistics and thus require the second bootstrap method. 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 synthetic data.