Year: 2026
Type: preprint
Abstract: We study $(\varepsilon,δ)$-differentially private synthetic data for arbitrary databases of $n$ records in $[-1,1]^d$ under a specified integral probability metric (IPM). We introduce generalized moment matching, which estimates moments privately, fits a probability measure, and samples synthetic records. A general error theorem applies when moment error controls the target IPM. This framework extends Chebyshev moment matching for $1$-Wasserstein distance and smooth queries. We apply the framework to maximum mean discrepancy with Matern and Laplace kernels and a two-layer ReLU neural tangent kernel. We also obtain guarantees for sliced Wasserstein-$1$ and the IPM induced by norm-bounded ReLU networks. With sufficiently many synthetic records,these rates are minimax optimal up to logarithmic factors for fixed dimension.
Source: arXiv (Cornell University)
Authors: Ding, Rundong, He, Yiyun, Zhu, Yizhe
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223341346