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Activity Number: 91 - Statistical Methods for Analysis of Time-Varying Network Data
Type: Invited
Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #322108 View Presentation
Title: Oracle Inequalities for the Dynamic Stochastic Block Model and Time-Dependent Graphon
Author(s): Marianna Pensky*
Companies: University of Central Florida
Keywords: dynamic network ; graphon ; stochastic block model ; non-parametric regression ; minimax rate

Networks arise in many areas of research such as sociology, biology, genetics, ecology, information technology to list a few. In this talk, we consider a dynamic network defined as an indirected graph with n nodes with connection probabilities changing in time. The objective of the present talk is estimation of the tensor A of the connection probabilities when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. Using vectorization of the model, in the context of DSBM, we derive penalized least squares estimator for the tensor A and show that the estimator satisfies oracle inequalities and also attains minimax lower bounds for the risk. We extend these results to the dynamic graphon. The estimators are adaptive to the unknown number of blocks in the context of DSBM or of the smoothness of the graphon function, and also preserve continuity between time points. In addition, all our results are non-asymptotic and allow a variety of extensions.

Authors who are presenting talks have a * after their name.

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