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Differentially Private Synthetic Data via Generalized Moment Matching

  • Rundong Ding
  • Yiyun He
  • Yizhe Zhu
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Abstract

We study (ε,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.

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Cite

BibTeXRIS
BibTeX
@misc{ding2026differentially,
  title = {{Differentially Private Synthetic Data via Generalized Moment Matching}},
  author = {Rundong Ding and Yiyun He and Yizhe Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30196},
  eprint = {2610.30196},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30196},
}
RIS
TY  - UNPB
TI  - Differentially Private Synthetic Data via Generalized Moment Matching
AU  - Rundong Ding
AU  - Yiyun He
AU  - Yizhe Zhu
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.30196
UR  - https://arxiv.org/abs/2610.30196
AB  - We study (ε,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.
ER  -