Privacy-preserving parametric inference for spatial autoregressive model

Spatial regression models are important tools in dealing with spatially dependent data and are widely used in many fields such as spatial econometric and regional science. When the spatial data contain sensitive information, the privacy of the data will be compromised along with the release of the analysis if appropriate privacy-preserving measures are not in place. In this paper, we study the privacy-preserving parametric inference for the spatial autoregressive model and propose corresponding differentially private algorithm. We construct a differentially private spatial autoregression framework that takes graph data into account. We improve the functional mechanism to be more accurate under the same degree of privacy protection. Theoretical analysis establishes both the privacy guarantees of the algorithm and the asymptotic normality of the estimation. Simulation and real data studies show improvements of our approach.