Abstract:
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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 flexible probabilistic framework that allows dependence among edges to propagate throughout the population graph. As specific examples, we introduce generalizations of beta-models with dependent edges capturing brokerage in social networks. On the statistical side, we derive the first consistency results in settings where dependence propagates throughout the population graph, and the number of parameters increases with the number of population members. The theoretical results are general and make weak assumptions, requiring nothing more than a strictly positive distribution with exponential parameterizations, and may be of independent interest. We showcase consistency results and convergence rates in the special case of generalized beta-models with dependent edges. On the computational side, we demonstrate how the conditional independence structure of models can be exploited for local computing.
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