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Differential privacy

Geometry-Adaptive Mechanisms for Private Synthetic Data

We generate private synthetic data by adapting to the geometry of the original dataset. This yields sharper error guarantees for data with low intrinsic dimension, while a sparse hierarchy keeps computation efficient.

University of Cambridge · Remote

Research with Dr. Amir Reza Asadi

Adapting to data geometry

Data in a high-dimensional space often lie on a much simpler, lower-dimensional set. We use this structure to generate synthetic data on [0,1]d under pure differential privacy. Our method privately selects the resolution of a spatial hierarchy and prunes it to adapt to the data’s geometry.

Under multiscale geometric assumptions, the expected Wasserstein error decreases at a rate governed by the support’s intrinsic dimension rather than only the ambient dimension. We also prove a lower bound showing that the dimension-dependent exponent is sharp under a corresponding geometric condition.

Geometry & accuracy

How geometry changes the error rate

Worst case

Ambient dimension

(εn)−1/d

The dimension of the surrounding space.

Geometry-adaptive

Packing-growth dimension

(εn)−1/k

The geometry of the data’s support.

Intrinsic structure can improve the dimension-dependent error rate.

Other work on differential privacy

I also study covariance estimation across separate data holders and private Gaussian sampling. The latter is the subject of my master’s thesis.

Related paper

2026

Geometry-Adaptive Mechanisms for Private Synthetic Data

R. Zare Moayedi, A. R. Asadi, M. H. Yassaee and G. Aminian

Preprint · Under review

arXiv
BibTeX
@misc{raoof_synthetic,
  title = {{Geometry-Adaptive Mechanisms for Private Synthetic Data}},
  author = {Zare Moayedi, Raoof and Asadi, Amir R. and Yassaee, Mohammad Hossein and Aminian, Gholamali},
  year = {2026},
  eprint = {2609.33363},
  archivePrefix = {arXiv},
  note = {Preprint; Under review}
}