Reveal-or-Obscure: A Differentially Private Sampling Algorithm

Naima Tasnim, Atefeh Gilani, Lalitha Sankar, Oliver Kosut

Keywords: Privacy, Sampling, Differential Privacy

Abstract: We introduce a differentially private algorithm called reveal-or-obscure (ROO) to generate a single representative sample from a dataset of $n$ observations drawn i.i.d. from an unknown discrete distribution $P$. Unlike methods that add explicit noise to the estimated empirical distribution, ROO achieves $\epsilon$-differential privacy (DP) by randomly choosing whether to "reveal" or "obscure" the empirical distribution. While ROO is structurally identical to Algorithm 1 proposed by (Cheu & Nayak, 2024), we prove a strictly better bound on the sampling complexity than that established in Theorem 12 of (Cheu & Nayak, 2024). To further improve the privacy-utility trade-off, we propose a novel generalized sampling algorithm called Data-Specific ROO (DS-ROO), where the probability of obscuring the empirical distribution of the dataset is chosen adaptively. We prove that DS-ROO satisfies $\epsilon$-DP, and provide empirical evidence that DS-ROO can achieve better utility under the same privacy budget of vanilla ROO.

Submission Number: 40