Differentially private graph publishing with degree distribution preservation

Abstract

The goal of privacy-preserving graph publishing is to protect individual privacy in released graph data while preserving data utility. Degree distribution, serving as fundamental operations for many graph analysis tasks, is a crucial data utility. Yet, existing methods using differential privacy (DP) cannot well preserve degree distribution, since they distill a graph into a set of structural statistics (e.g. dK-series, etc.) that only captures local degree correlations, and require massive noise added to mask the change of a single edge. Recently Generative Adversarial Network for graphs (NetGAN) plays a key role in machine learning, due to its ability to capture the local and global degree distribution of the graph via biased random walks. Further, it allows us to move the burden of privacy-preserving to the learning procedure of its discriminator, rather than the extracted structure features. Inspired by this, we propose Priv-GAN, a private publishing model based on NetGAN. Instead of distilling and then publishing graphs, we publish the Priv-GAN model that is trained using the original data in a DP manner. With Priv-GAN, data holders are able to produce synthetic graph data with degree distribution preservation. Compared to alternative solutions, ours highlights that (i) a private Langevin with gradient estimate is designed as an optimizer for discriminator, which provides a theoretical gradient upper bound and achieves DP by adding noise to the gradients; and (ii) importantly, the error bound of the noisy Langevin method is theoretically analyzed, which demonstrates that with appropriate parameter settings, Priv-GAN is able to maintain high utility guarantees. Experimental results confirm our theoretical findings and the efficacy of Priv-GAN.