Title: Generalized beta-models with dependent edges and parameter vectors of increasing dimension
Authors: Jonathan Stewart - Rice University (United States) [presenting]
Michael Schweinberger - Department of Statistics, Rice University (United States)
Abstract: An important question in statistical network analysis is how to construct random graph models with dependent edges without sacrificing computational scalability and statistical guarantees. We advance models, methods, and theory by introducing a probabilistic framework for populations consisting of overlapping subpopulations of similar or dissimilar sizes, which allows dependence to propagate throughout the population graph. As examples, we introduce generalizations of beta-models with dependent edges capturing brokerage in social networks. On the statistical side, we derive consistency results in settings where dependence propagates throughout the population graph, and the number of parameters increases with the number of subpopulations. We show how the rate of convergence depends on the amount of overlap and the sizes of subpopulations, how different the sizes are, and how sparse the population graph is. On the computational side, we demonstrate how the conditional independence structure of models can be exploited for local computing.