这篇论文分析了GP后验采样的隐私性，不用额外加噪就能获得DP保证，还给了Rényi-DP界限。和标准加噪方法比，它更巧妙地利用了内生随机性。
该研究分析了高斯过程（GP）后验采样中释放样本路径的差分隐私（DP）性质。与标准DP机制不同，后验采样的内在随机性可提供隐私保证。作者推导了显式的Rényi-DP界限，将隐私泄露分解为后验均值依赖和后验协方差依赖部分，并指出有效岭正则化对隐私有显著影响。通过成员推理攻击实验，验证了隐私泄露与正则化强度、后验方差及释放样本路径数量之间的预测关系。在噪声观测任务中，隐私兼容的正则化在保持有用决策的同时仅带来适度效用损失。
Differential Privacy of Gaussian Process Posterior Sampling
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 Rényi-DP bounds for GP posterior sample-path release. The bounds separate posterior-mean leakage from data-dependent posterior-covariance leakage showing that meaningful privacy depends sharply on effective ridge regularisation. We apply membership-inference attacks to show that empirical leakage follows the predicted dependence on regularisation, posterior variance and the number of released posterior sample-paths. Utility experiments on downstream posterior-sampling tasks identify noisy-observation regimes where privacy-compatible regularisation preserves useful decisions with modest utility loss. When stronger privacy is needed, the intrinsic guarantee can be sharpened by adding calibrated GP noise, providing an explicit additional privacy knob.