Differential Privacy of Gaussian Process Posterior Sampling (opens in new tab)

We study the privacy of releasing posterior sample paths from a Gaussian process (GP) when the entire training set including covariates and responses is private. Unlike standard differential-privacy (DP) mechanisms that add external noise, posterior sampling is random by construction. We show that this intrinsic randomness yields DP guarantees by deriving explicit R\'enyi-DP bounds for GP posterior sample-path release. The bounds separate post...