Abstract:
<p>This thesis presents spatially and temporally dependent hierarchical Bayesian models for the analysis of social networks and associated textual data. Social network analysis has received significant recent attention and has been applied to fields as varied as analysis of Supreme Court votes, Congressional roll call data, and inferring links between authors of scientific papers. In many traditional social network analysis models, temporal and spatial dependencies are not considered due to computational difficulties, even though significant such dependencies often play a significant role in the underlying generative process of the observed social network data.</p><p>Thus motivated, this thesis presents four new models that consider spatial and/or temporal dependencies and (when available) the associated text. The first is a time-dependent (dynamic) relational topic model that models nodes by their relevant documents and uses probit regression construction to map topic overlap between nodes to a link. The second is a factor model with dynamic random effects that is used to analyze the voting patterns of the United States Supreme Court. hTe last two models present the primary contribution of this thesis two spatially and temporally dependent models that jointly analyze legislative roll call data and the their associated legislative text and introduce a new paradigm for social network factor analysis: being able to predict new columns (or rows) of matrices from the text. The first uses a nonparametric joint clustering approach to link the factor and topic models while the second uses a text regression construction. Finally, two other models on analysis of and tracking in video are also presented and discussed.</p>
