On Inherent Privacy of Posterior Sampling: A Unified Rényi-Divergence Framework
Differential Privacy (DP) provides a rigorous framework for quantifying privacy guarantees. While most methods achieve DP by injecting calibrated random noise, the intrinsic randomness of certain procedures such as sampling can yield DP guarantees ``for free''. In this work, we develop a unified Rényi divergence framework to characterize the inherent DP guarantees of sampling from a Bayesian posterior distribution. We show that the privacy loss incurred by One-Posterior-Sampling (OPS) is governed by posterior exponential moments of the single-record log-likelihood ratio, and establish explicit DP guarantees under uniformly bounded, sub-Gaussian, or sub-exponential tail regimes. We apply t...
| Authors | Ruyu Zhou, Fang Liu |
|---|---|
| Primary category | stat.ML |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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