Geometry-Adaptive Mechanisms for Private Synthetic Data
Generating differentially private synthetic data with meaningful Wasserstein utility guarantees is challenging in high dimensions. For datasets of size \(n\) on $[0,1]^d$ with $d\ge2$, existing pure \(\varepsilon\)-differentially private mechanisms achieve expected $1$-Wasserstein error of order $(\varepsilon n)^{-1/d}$, reflecting the curse of dimensionality. While this rate is optimal in the worst case, it can be overly pessimistic when the data are supported on a lower-dimensional set. We formalize this through a multiscale packing-growth dimension $k$, which captures the geometric complexity of the support via the growth of packing numbers across scales. We propose \emph{Adaptive Prun...
| Authors | Raoof Zare Moayedi, Amir R. Asadi, Mohammad Hossein Yassaee et al. |
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| Primary category | cs.DS |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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