Algorithmically Effective Differentially Private Synthetic Data
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We present a highly effective algorithmic approach for generating ε-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. In particular, for a dataset X in the hypercube [0,1]^d, our algorithm generates synthetic dataset Y such that the expected 1-Wasserstein distance between the empirical measure of X and Y is O((ε n)^-1/d) for d≥ 2, and is O(log^2(ε n)(ε n)^-1) for d=1. The accuracy guarantee is optimal up to a constant factor for d≥ 2, and up to a logarithmic factor for d=1. Our algorithm has a fast running time of O(ε n) for all d≥ 1 and demonstrates improved accuracy compared to the method in (Boedihardjo et al., 2022) for d≥ 2.
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