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Abstract Details

Activity Number: 50
Type: Invited
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #303642
Title: Maximum Likelihood Estimation in Network Models
Author(s): Alessandro Rinaldo*+
Companies: Carnegie Mellon University
Address: Department of Statistics, Pittsburgh, PA, 15213, USA

This talk is concerned with maximum likelihood estimation in exponential statistical models for networks (random graphs) and, in particular, with the beta model, a simple model for undirected graphs in which the degree sequence is the minimal sufficient statistic. I will present necessary and sufficient conditions for the existence of the MLE of the beta model parameters that are based on a geometric object known as the polytope of degree sequences. Using this result, it is possible to characterize in a combinatorial fashion sample points leading to a nonexistent MLE and non-estimability of the probability parameters under a nonexistent MLE. I will further indicate some conditions guaranteeing that the MLE exists with probability tending to one as the number nodes increases. Much of this analysis applies also to other well-known models for networks, such as the Rasch model, the Bradley-Terry model and the more general p1 model of Holland and Leinhardt. These results are in fact instantiations of rather general geometric properties of exponential families with polyhedral support that will be illustrated with a simple exponential random graph model.

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