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Differentially Private Sampling from Distributions
Satchit Sivakumar · Marika Swanberg · Sofya Raskhodnikova · Adam Smith
We initiate an investigation of private sampling from distributions. Given a dataset with $n$ independent observations from an unknown distribution $P$, a sampling algorithm must output a single observation from a distribution that is close in total variation distance to $P$ while satisfying differential privacy. Sampling abstracts the goal of generating small amounts of realistic-looking data. We provide upper and lower bounds for the dataset size needed for this task for two natural families of distributions: arbitrary distributions on $\{1,\ldots ,k\}$ and product distributions on $\{0,1\}^d$. We demonstrate that, in some parameter regimes, private sampling requires asymptotically fewer observations than learning a description of $P$ nonprivately; in other regimes, however, sampling proves to be as difficult as private learning.

Author Information

Satchit Sivakumar (Boston University)
Marika Swanberg (Boston University)
Sofya Raskhodnikova (Pennsylvania State Univ University Park)
Adam Smith (Boston University)

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