Abstract

There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models.

In this talk I will relate the properties of ERG models to the properties of the broader class of discrete exponential families. I will describe a general geometric result about discrete exponential families with polyhedral support. I will show how the properties of these families can be well captured by some fundamental geometric objects of polyhedral form.

I will discuss the relevance of such results to maximum likelihood estimation, both from a theoretical and computational standpoint. I will then apply these results to the analysis of ERG models. By means of a detailed example, I will provide some characterization and a partial explanation of certain pathological features of ERG models known as degeneracy.

Joint work with S.E. Fienberg and Y. Zhou

Venue, Date, and Time

Venue: GHC 6115

Date: Monday, November 9, 2009

Time: 12:00 noon