Differentially Private Exponential Random Graphs
This work addresses privacy concerns for social network data users, but it is incremental as it applies existing differential privacy techniques to a specific model class.
The authors tackled the problem of protecting individual relationships in social networks by proposing methods to release and analyze synthetic graphs with differential privacy, specifically using randomized response for ε-edge differential privacy and likelihood-based inference with MCMC to fit exponential random graph models, demonstrating utility on real data.
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 $ε$-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.