Differentially Private Sampling from Distributions
Sofya Raskhodnikova, Satchit Sivakumar, Adam Smith, Marika Swanberg · SIAM Journal on Computing · 2025
Abstract. We initiate an investigation of private sampling from distributions. Given a dataset with [Formula: see text] independent observations from an unknown distribution [Formula: see text], a sampling algorithm must output a single observation from a distribution that is close in total variation distance to [Formula: see text] while satisfying differential privacy. Sampling abstracts the goal of generating small amounts of realistic-looking data. We provide tight upper and lower bounds for the dataset size needed for this task for three natural families of distributions: arbitrary distributions on [Formula: see text], arbitrary product distributions on [Formula: see text], and product distributions on [Formula: see text] with bias in each coordinate bounded away from 0 and 1. We demonstrate that, in some parameter regimes, private sampling requires asymptotically fewer observations than learning a description of [Formula: see text] nonprivately; in other regimes, however, private sampling proves to be as difficult as private learning. Notably, for some classes of distributions, the overhead in the number of observations needed for private learning compared to nonprivate learning is completely captured by the number of observations needed for private sampling.