[Submitted on 21 Oct 2026 (v1), last revised 23 Oct 2026 (this version, v2)]
Abstract:We study $(varepsilon,delta)$-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.
Submission history
From: Yiyun He [view email]
[v1] Wed, 21 Oct 2026 07:06:03 UTC (66 KB)
[v2] Fri, 23 Oct 2026 03:34:17 UTC (66 KB)
