Differentially Private Sampling from Distributions via Wasserstein Projection
Provides a new theoretical framework and optimal mechanism for differentially private sampling, improving utility for distributions with geometric or support differences.
This paper addresses differentially private sampling using Wasserstein distance instead of KL divergence, overcoming limitations in capturing geometric structure and handling differing supports. The proposed Wasserstein Projection Mechanism achieves minimax optimality with efficient approximation algorithms.
In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such formulations suffer from two key limitations: 1) they fail to capture the geometric structure of the support, and 2) they are not applicable when the supports of the distributions differ. To deal with these issues, we develop a novel framework for DP sampling with Wasserstein distance as the utility measure. In this formulation, we propose Wasserstein Projection Mechanism (WPM), a minimax optimal mechanism based on Wasserstein projection. Furthermore, we develop efficient algorithms for computing the proposed mechanisms approximately and provide convergence guarantees.