Inference in Nonparametric Latent Variable Network Models

• Activity Number: 670
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sharmodeep Bhattacharyya* and Peter J. Bickel and Patrick J. Wolfe
• Companies: Oregon State University and UC Berkeley and University College London
• Keywords: Networks ; Nonparametrics ; Community detection ; graphon ; Subgraph Count ; Block Model

Abstract

Analysis of stochastic models of networks has become quite important in light of the huge influx of network data in social, information and bio sciences. Latent variable network models provide a general nonparametric class of models for unlabeled random graphs. Approximation with stochastic block models gives one way to estimate the nonparametric network models. We show that as long as the fitting method of block model satisfies certain consistency properties, we can have consistent estimators for parameters of the nonparametric network models. We also propose cross-validation methods using count statistics to regularize the fitted block models. The proposed cross-validation methods are independent of the algorithm used to fit the block model and thus can also be used to choose the number of communities in community detection algorithms. Investigation is also done when number of communities vary with number of vertices as well as for more general block models like overlapping block models. Simulation study and illustration of inference on real networks are also provided.