Differentially Private Sampling from Distributions via Wasserstein Projection

• URL: http://arxiv.org/abs/2605.10015v1
• Date: Mon, 11 May 2026 05:40:36 GMT
• Title: Differentially Private Sampling from Distributions via Wasserstein Projection
• Abstract summary: We develop a novel framework for DP sampling with Wasserstein distance as the utility measure.<n>In this paper, we propose Wasserstein Projection Mechanism (WPM), a minimax optimal mechanism based on Wasserstein projection.
• Score: 5.026439970933249
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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