Differential Privacy of Gaussian Process Posterior Sampling

Researchers have found that Gaussian process posterior sampling provides differential privacy guarantees without adding external noise, with effective ridge regularisation being crucial for meaningful privacy.

A study on arXiv^[1] shows that the intrinsic randomness of posterior sampling yields differential-privacy (DP) guarantees. The researchers derived explicit Rényi-DP bounds for GP posterior sample-path release, highlighting the importance of effective ridge regularisation. They also applied membership-inference attacks to demonstrate that empirical leakage follows the predicted dependence on regularisation, posterior variance, and the number of released posterior sample-paths. Another study on arXiv^[2] found that current practices for reporting differential privacy guarantees are incomplete and potentially misleading. The authors propose using Gaussian Differential Privacy (GDP) to capture the entire privacy profile of DP-SGD and related algorithms with virtually no error. GDP can provide non-asymptotic bounds on privacy guarantees using numerical accountants, and the authors investigate the privacy profiles of state-of-the-art DP large-scale image classification and the TopDown algorithm for the U.S. Decennial Census.