AMS Seminar: Walter Dempsey (Harvard University) @ Whitehead 304
Title: “Statistical network modeling via exchangeable interaction processes”
Many modern network datasets arise from processes of interactions in a population, such as phone calls, e-mail exchanges, co-authorships, and professional collaborations. In such interaction networks, the interactions comprise the fundamental statistical units, making a framework for interaction-labeled networks more appropriate for statistical analysis. In this talk, we present exchangeable interaction network models and explore their basic statistical properties. These models allow for sparsity and power law degree distributions, both of which are widely observed empirical network properties. I will start by presenting the Hollywood model, which is computationally tractable, admits a clear interpretation, exhibits good theoretical properties, and performs reasonably well in estimation and prediction.
In many settings, the series of interactions are structured. E-mail exchanges, for example, have a single sender and potentially multiple receivers. I will introduce hierarchical exchangeable interaction models for the study of structured interaction networks. In particular, I will introduce the Enron model as a canonical example, which partially pools information via a latent, shared population-level distribution. A detailed simulation study and supporting theoretical analysis provide clear model interpretation, and establish global power-law degree distributions. A computationally tractable Gibbs sampling algorithm is derived. Inference will be shown on the Enron e-mail dataset. I will end with a discussion of how to perform posterior predictive checks on interaction data. Using these proposed checks, I will show that the model fits the data well.