用最优的水距离机制实现隐私保护采样，解决传统方法几何结构失真问题。
Differentially Private Sampling from Distributions via Wasserstein Projection
- 以水距离为度量设计隐私采样新框架
- 提出极小极大最优的投影机制，支持不同支撑集分布
- 算法高效可近似计算，有收敛保证，适合隐私敏感数据生成
本文研究在差分隐私约束下从分布中采样的问题。以往工作多采用基于密度比的度量（如KL散度）衡量隐私采样效用，但这类方法存在两大缺陷：一是无法捕捉支撑集的几何结构，二是当分布支撑集不同时无法适用。为此，我们提出以水距离作为效用度量的新框架，并设计了基于水距离投影的极小极大最优机制——水距离投影机制（WPM）。此外，我们开发了该机制的高效近似计算算法，并提供了收敛性保证。
原文摘要 · Abstract (English)
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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