Differentially Private Synthetic Data via Generalized Moment Matching

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 this http URL 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.

Machine Learning (stat.ML); Information Theory (cs.IT); Machine Learning (cs.LG); Probability (math.PR); Statistics Theory (math.ST)

arXiv:2610.30196 [stat.ML]

(or arXiv:2610.30196v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.30196 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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