SRL2004: Statistical Relational Learning and
its Connections to Other Fields

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Statistical Models for Social Networks

Mark Handcock
University of Washington

This talk is an overview of social network analysis from the perspective of a statistician.

The main focus is on the conceptual and methodological contributions of the social network community going back over eighty years. The field is, and has been, broadly multidisciplinary with significant contributions from the social, natural and mathematical sciences. This has lead to a plethora of terminology, and network conceptualizations commensurate with the varied objectives of network analysis. As a primary focus of the social sciences has been the representation of social relations with the objective of understanding social structure, social scientists have been central to this development.

We review statistical exponential family models that recognize the complex dependencies within relational data structures. We consider three issues: the specification of realistic models, the algorithmic difficulties of the inferential methods, and the assessment of the degree to which the graph structure produced by the models matches that of the data. Insight can be gained by considering model degeneracy and inferential degeneracy for commonly used estimators.