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This paper proposes SPLICE, a differentially private synthetic data method that matches noisy sliced Chebyshev moments and claims a Sliced Wasserstein-1 error bound of Õ(1/√n) that does not depend on data dimension. For ML practitioners, the notable part is the dimension-independent global guarantee, which addresses the exponential cost that has limited prior methods, though the results are theoretical and the practical gains rest on the authors' benchmark. Readers building privacy-preserving training or data-sharing pipelines should watch for whether the approach holds up outside that benchmark.
Differentially Private Synthetic Data from Sliced Chebyshev Moments
arXiv:2610.42081v1 Announce Type: new Abstract: Research on practical differentially private (DP) synthetic data has largely focused on methods that approximately preserve low-dimensional marginals of a target distribution, and can thus only hope to preserve higher-dimensional, global structure as a lucky by-product. At the same time, existing methods that target global accuracy guarantees pay a price exponential in the data dimension, $d$. In this work, we address this ``curse of dimensionality'' by presenting a new DP synthetic data algorithm, SPLICE, that comes with a compelling global distributional guarantee, even in high-dimensions, and moreover, is practically state-of-the-art. Our algorithm is based on measuring noisy sliced Chebyshev polynomial moments of the target distribution and fitting a distribution to match, a twist on recent polynomial methods for 1-D synthetic data. We prove that, given a dataset of $n$ examples, SPLICE returns a private distribution with Sliced Wasserstein-1 distance $\tilde{O}(1/\sqrt{n})$ from the target, for constant privacy parameters. Notably, this bound is independent of the data dimension, $d$. Along the way, we prove a moment matching result of independent interest: for a distribution on the unit ball, matching the first $O(1/\alpha)$ Chebyshev moments along $\tilde{O}(d/\alpha^2)$ random directions guarantees $\alpha$ Sliced Wasserstein error. Finally, we provide a practical implementation of the algorithm that borrows tools from the tensor decomposition literature and achieves state-of-the-art performance compared to prior DP synthetic data methods on an extensive benchmark.
Abstract:Research on practical differentially private (DP) synthetic data has largely focused on methods that approximately preserve low-dimensional marginals of a target distribution, and can thus only hope to preserve higher-dimensional, global structure as a lucky by-product. At the same time, existing methods that target global accuracy guarantees pay a price exponential in the data dimension, $d$. In this work, we address this ``curse of dimensionality'' by presenting a new DP synthetic data algorithm, SPLICE, that comes with a compelling global distributional guarantee, even in high-dimensions, and moreover, is practically state-of-the-art. Our algorithm is based on measuring noisy sliced Chebyshev polynomial moments of the target distribution and fitting a distribution to match, a twist on recent polynomial methods for 1-D synthetic data. We prove that, given a dataset of $n$ examples, SPLICE returns a private distribution with Sliced Wasserstein-1 distance $\tilde{O}(1/\sqrt{n})$ from the target, for constant privacy parameters. Notably, this bound is independent of the data dimension, $d$. Along the way, we prove a moment matching result of independent interest: for a distribution on the unit ball, matching the first $O(1/\alpha)$ Chebyshev moments along $\tilde{O}(d/\alpha^2)$ random directions guarantees $\alpha$ Sliced Wasserstein error. Finally, we provide a practical implementation of the algorithm that borrows tools from the tensor decomposition literature and achieves state-of-the-art performance compared to prior DP synthetic data methods on an extensive benchmark.
Machine Learning (cs.LG); Computers and Society (cs.CY); Data Structures and Algorithms (cs.DS)
G.3; I.2.6; G.1.2; K.4.1
arXiv:2610.42081 [cs.LG]
(or arXiv:2610.42081v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.42081 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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