Differentially private synthesis of Spatial Point Processes

TL;DR

This paper introduces differentially private methods for synthesizing spatial point pattern data, ensuring privacy while maintaining data utility, applicable to various models and linear networks.

Contribution

It proposes novel DP-based Poisson and Cox point synthesizers with an $oldsymbol{ extalpha}$-neighborhood concept, extending privacy guarantees to spatial point pattern synthesis.

Findings

Effective privacy-utility trade-off demonstrated in simulations

Synthesizers work on linear networks

Provides parameter conditions for differential privacy

Abstract

This paper proposes a method to generate synthetic data for spatial point patterns within the differential privacy (DP) framework. Specifically, we define a differentially private Poisson point synthesizer (PPS) and Cox point synthesizer (CPS) to generate synthetic point patterns with the concept of the $\alpha$-neighborhood that relaxes the original definition of DP. We present three example models to construct a differentially private PPS and CPS, providing sufficient conditions on their parameters to ensure the DP given a specified privacy budget. In addition, we demonstrate that the synthesizers can be applied to point patterns on the linear network. Simulation experiments demonstrate that the proposed approaches effectively maintain the privacy and utility of synthetic data.