Differentially Private Exponential Random Graphs

TL;DR

This paper introduces methods for generating differentially private synthetic social network graphs using ERGMs, ensuring privacy while maintaining utility for statistical analysis through MCMC techniques.

Contribution

It develops a framework combining randomized response and likelihood-based inference to fit ERGMs under differential privacy guarantees.

Findings

Effective privacy protection via $oldsymbol{ extepsilon}$-edge differential privacy.

Successful application of MCMC for ERGM fitting on synthetic graphs.

Demonstrated utility of the methods on real social network data.

Abstract

We propose methods to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network. Proposed techniques aim at fitting and estimating a wide class of exponential random graph models (ERGMs) in a differentially private manner, and thus offer rigorous privacy guarantees. More specifically, we use the randomized response mechanism to release networks under $\epsilon$-edge differential privacy. To maintain utility for statistical inference, treating the original graph as missing, we propose a way to use likelihood based inference and Markov chain Monte Carlo (MCMC) techniques to fit ERGMs to the produced synthetic networks. We demonstrate the usefulness of the proposed techniques on a real data example.