Abstract:
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The question of how to construct models of random graphs with dependent edges without sacrificing computational scalability and statistical guarantees is an important question that has received scant attention. In this talk, I present recent advancements in models, methods, and theory for modeling networks with dependent edges. On the modeling side, I introduce a novel probabilistic framework for specifying edge interactions that allows dependence to propagate throughout the population graph, with applications to brokerage in social networks. On the statistical side, I obtain 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. Last, but not least, on the computational side I demonstrate how the conditional independence structure of models can be exploited for local computing on subgraphs, which facilitates parallel computing on multi-core computers or computing clusters.
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