Algorithmically Effective Differentially Private Synthetic Data

We present a highly effective algorithmic approach for generating epsilon-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((epsilon n)(-1/d)) for d >= 2, and is O(log(2) (epsilon n)(epsilon 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(epsilon dn) for all d >= 1 and demonstrates improved accuracy compared to the method in (Boedihardjo et al., 2022c) for d >= 2.