Exponential random graph estimation under differential privacy

Abstract

The effective analysis of social networks and graph-structured data is often limited by the privacy concerns of individuals whose data make up these networks. Differential privacy offers individuals a rigorous and appealing guarantee of privacy. But while differentially private algorithms for computing basic graph properties have been proposed, most graph modeling tasks common in the data mining community cannot yet be carried out privately. In this work we propose algorithms for privately estimating the parameters of exponential random graph models (ERGMs). We break the estimation problem into two steps: computing private sufficient statistics, then using these to estimate the model parameters. We consider recent specifications of ERGMs and show that our perturbation method, the chain mechanism, offers provably less error than comparable methods. In addition, our redesigned estimation algorithm considers the noise distribution of the private statistics and offers better accuracy than directly performing parameter estimation on the statistics. © 2014 ACM.