Variational Methods for Modeling Large Networks

• Activity Number: 289
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Duy Q. Vu and David R. Hunter* and Michael Schweinberger
• Companies: The University of Melbourne and Penn State and Rice University
• Keywords: Mixture Models ; MM algorithms

Abstract

We describe recent advances in the application of variational methods to the approximate maximum likelihood estimation of mixture models for large networks with more than a hundred thousand nodes. Relative to alternative model-based clustering methods for networks, we introduce a more flexible modeling framework, improve the variational-approximation estimation algorithm, discuss and implement standard error estimation via a parametric bootstrap approach, and apply these methods to much larger datasets than those seen elsewhere in the literature. The more flexible modeling framework is achieved through introducing novel parameterizations of the model, giving varying degrees of parsimony, using exponential family models whose structure may be exploited in various theoretical and algorithmic ways. The algorithms, which we show how to adapt to the more complicated optimization requirements introduced by the constraints imposed by the novel parameterizations we propose, are based on variational generalized EM algorithms, where the E-steps are augmented by a minorization-maximization (MM) idea.