Differentially private graphical degree sequences and synthetic graphs

Increasing volumes of personal and sensitive data are collected and archived by health networks, government agencies, search engines, social networking websites, and other organizations. The social networks, in particular, are a prominent source of data for researchers in economics, epidemiology, sociology and many other disciplines and have sparked a flurry of research in statistical methodology for network analysis. While the social benefits of analyzing these data are significant, their release can be devastating to the privacy of individuals and organizations. In this talk, we give a brief overview of challenges associated with protecting confidential data, and the problem of releasing summary statistics of graphs needed to build statistical models for networks while preserving privacy of individual relations. We present an algorithm for releasing graphical degree sequences of simple undirected graphs under the framework of differential privacy. The algorithm is designed to provide utility for statistical inference in random graph models whose sufficient statistics are functions of degree sequences. Specifically, we focus on the tasks of existence of maximum likelihood estimates, parameter estimation and goodness-of-fit testing for the beta model of random graphs. We show the usefulness of our algorithm by evaluating it empirically on simulated and real-life datasets. As the released degree sequence is graphical, our algorithm can also be used to release synthetic graphs under the beta model.
(Joint work with Vishesh Karwa)

Event Topic

Nonlinear Algebra and Statistics (NLASTATS)