A Differentially Private Graph Estimator

Abstract

We consider the problem of making graph databases such as social network structures available to researchers for knowledge discovery while providing privacy to the participating entities. We show that for a specific parametric graph model, the Kronecker graph model, one can construct an estimator of the true parameter in a way that both satisfies the rigorous requirements of differential privacy and is asymptotically efficient in the statistical sense. The estimator, which may then be published, defines a probability distribution on graphs. Sampling such a distribution yields a synthetic graph that mimics important properties of the original sensitive graph and, consequently, could be useful for knowledge discovery.

No free lunch in data privacy

“…For social networks, examples include [17,27,30]. Rastogi et al [30] proposed a relaxation of differential privacy for social networks by proving an equivalence to adversarial privacy (which makes assumptions about the data), and then adding further constraints on the data-generating mechanism.…”

A differentially private estimator for the stochastic Kronecker graph model

“…We attempted to use the method of using stochastic graph models to generate private "synthetic" graphs [17] but were unable to provide a useful upper bound on the global sensitivity of the Maximum Likelihood Estimator or an approximation of the MLE of the Stochastic Kronecker graph model used by Leskovec et al [15]. Consequently, we were unable to use those ideas to actually model a real-world graph and release the estimator in a differentially private manner.…”

“…We first formalize the idea that the output of the estimator should not change significantly if a link between two individuals is included or excluded from the observations. Definition 4.1 (Edge neighborhood [9,17]). Given a graph G(V, E), the (edge) neighborhood of a graph is the set…”

“…Private estimation of the Stochastic Kronecker Graph (SKG) model parameter is an interesting problem, especially given the surge in the popularity of SKGs for graph modeling. Our initial attempt at private SKG estimation [17] was based on the Kronecker graph estimator of Leskovec and Faloutsos [15]. However, our solution was inefficient because we did not have any practical way of bounding the global sensitivity of the required parameters.…”

Publishing Attributed Social Graphs with Formal Privacy Guarantees

“…Request permissions from permissions@acm.org. degree distribution [11], subgraph counting [13,2], clustering coefficient [35], and frequent subgraph mining [33]; and (2) private graph release, which typically involves (privately) fitting a generative graph model to input graphs in order to sample a synthetic graph, which can be used in analyses as a proxy for a real input graph (e.g., [23,30,34,4,36,18,29]). We follow this latter approach.…”