Statistics Department Hosted Seminar Series by Professor Yves Atchade: Sharmodeep Bhattacharyya, Statistical Inference of Nonparametric Latent Variable Network Models

Professor Yves Atchade is hosting a bi-weekly seminar series called "Statistical Computing" which will discuss how statistical methods are implemented, and to explore computational techniques with potential applications in statistics

Analysis of stochastic models of networks is 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. Our main goal in this work is to present an unified framework for inference under the nonparametric latent variable network models. One approach is use of integral parameters and count statistics.  We consider subsampling bootstrap methods for finding empirical distribution of count features or `moments' (Bickel, Chen and Levina, AoS, 2011) (such as number of triangles) and smooth functions of these moments for the networks. Using these methods, we can not only estimate variance of count features but also get good estimates of such feature counts, which are usually prohibitive to compute numerically in large networks. We also try to approximate the exchangeable network models by stochastic block models and we show that as long as fitting method of block model satisfies certain consistency properties, we can have consistent estimators for parameters of the network model. We also propose a cross-validation method using count statistics to regularize the fitted block models and choose the size of the block models approximating the nonparametric model. The cross-validation method provides us with a procedure to regularize the fitted block models independent of the algorithm used to fit the block model. A simulation study and illustration of inference on real networks are also provided.

(Joint work with Peter Bickel and Patrick Wolfe)