Stabilizing the Poisson point synthesizer, particularly the Laplace mechanism

Improve the stability of the Poisson point synthesizer—a randomized mechanism that generates synthetic spatial point patterns by simulating a Poisson point process with an intensity derived from the original data—particularly for the Laplace mechanism approach, which currently tends to generate an excessive number of synthetic points.

Background

The paper introduces differentially private point synthesizers for spatial point patterns, including Poisson point synthesizers (PPS) and Cox point synthesizers (CPS). Among the approaches, the Laplace mechanism is highlighted as achieving pure differential privacy. However, empirical results show that the Laplace mechanism often generates substantially more synthetic points than the original datasets, especially under small privacy budgets, which raises concerns about stability and practical usability.

In the conclusion, the authors explicitly note that improving the stability of the Poisson point synthesizer remains an unresolved issue, emphasizing the Laplace mechanism's tendency to overproduce points. They mention thinning as a potential remedy but indicate that determining an appropriate thinning probability requires further investigation, underscoring the open nature of this problem.