Differentially private estimation in a class of bipartite graph models

In bipartite networks, nodes are divided into two different sets (namely, a set of actors and a set of events), and edges exist only between actors and events. The degree sequence of bipartite graph models may contain sensitive information. Thus, it is desirable to release noisy degree sequence, not the original degree sequence, in order to decrease the risk of privacy leakage. In this article, we propose to release the degree sequence in general bipartite graphs by adding discrete Laplace noises, which satisfies differential privacy. We use the moment method to estimate the unknown model parameter. The resulted estimator satisfies differential privacy. We establish the consistency and asymptotic normality of the differentially private estimator when the number of nodes goes to infinity. Finally, we apply our theoretical results to the logistic model and the log -linear model.