Exploration of large networks with covariates via fast and universal latent space model fitting

Abstract: Latent space models are effective tools for statistical network data analysis. The present paper presents two fitting algorithms for a broad class of latent space models that can effectively model network characteristics such as degree heterogeneity, transitivity, homophily, etc. The methods are motivated by inner-product models, but are readily applicable to more general models that allow latent vectors to affect edge formation in flexible ways. Both methods are scalable to very large networks and have fast rates of convergence. The effectiveness of the modeling approach and fitting methods is demonstrated on a number of simulated and real world network datasets.