Differentially Private Sampling from Distributions via Wasserstein Projection
2026-05-11 • Cryptography and Security
Cryptography and SecurityMachine Learning
AI summaryⓘ
The authors study how to create private samples from a data distribution while keeping the samples useful. Previous methods used measures that don't work well if the shape or support of data changes. They introduce a new way to measure usefulness using Wasserstein distance, which captures geometric differences. They also propose a method called the Wasserstein Projection Mechanism, which is proven to be optimal, and provide algorithms to compute it with guaranteed accuracy.
Differential PrivacySamplingWasserstein DistanceMinimax OptimalityKL DivergenceGeometric StructureProbability Distribution SupportProjection MechanismConvergence Guarantees
Authors
Shokichi Takakura, Seng Pei Liew, Satoshi Hasegawa
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.