aiqbench analysis
This research establishes that the intrinsic randomness in Gaussian process posterior sampling offers inherent differential privacy guarantees without requiring external noise injection. By deriving Rényi-DP bounds, the study isolates how regularization strength and covariance scales control privacy leakage, confirming these mechanisms against membership inference attacks. The findings demonstrate a "privacy for free" regime in large-data asymptotics where utility is preserved alongside vanishing privacy risks.
Differential Privacy of Gaussian Process Posterior Sampling
arXiv:2606.17995v2 Announce Type: replace-cross Abstract: We study the privacy of releasing functional 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 inject external noise, posterior sampling is intrinsically random and we show that this randomness provides useful privacy guarantees. We derive R\'enyi-DP guarantees separating privacy leakage through the posterior mean from a distinct channel induced by the data-dependent posterior covariance. The analysis identifies effective ridge regularisation and covariance scale as the principal privacy-controlling quantities and yields sharper guarantees in several regimes of practical interest as well as extensions to repeated and adaptive releases. Membership inference attacks confirm the predicted dependence on regularisation, covariance scale and the number of released paths. Utility experiments on downstream posterior sampling tasks identify noisy observation regimes where privacy-compatible regularisation preserves useful samples. Finally we identify large-data asymptotic regime in which the privacy parameter and posterior mean-square risk vanish simultaneously, yielding privacy for free. Together, these results provide a comprehensive characterisation of privacy and utility of GP posterior sampling.
Abstract:We study the privacy of releasing functional 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 inject external noise, posterior sampling is intrinsically random and we show that this randomness provides useful privacy guarantees. We derive Rényi-DP guarantees separating privacy leakage through the posterior mean from a distinct channel induced by the data-dependent posterior covariance. The analysis identifies effective ridge regularisation and covariance scale as the principal privacy-controlling quantities and yields sharper guarantees in several regimes of practical interest as well as extensions to repeated and adaptive releases. Membership inference attacks confirm the predicted dependence on regularisation, covariance scale and the number of released paths. Utility experiments on downstream posterior sampling tasks identify noisy observation regimes where privacy-compatible regularisation preserves useful samples. Finally we identify large-data asymptotic regime in which the privacy parameter and posterior mean-square risk vanish simultaneously, yielding privacy for free. Together, these results provide a comprehensive characterisation of privacy and utility of GP posterior sampling.
8 pages of main text + 37 pages appendix. Expanded theory (sharper specialised bounds and privacy-for-free theorems)
Machine Learning (stat.ML); Cryptography and Security (cs.CR); Machine Learning (cs.LG)
arXiv:2606.17995 [stat.ML]
(or arXiv:2606.17995v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2606.17995 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 290 words
Related coverage
Differential Privacy of Gaussian Process Posterior Sampling
arXiv · Jun 17, 2026
Exploiting Gradients in Bayesian Inference of Expensive Simulators
arXiv · Oct 9, 2026
StochLOB: Heavy-Tailed Score Matching for Robust Limit Order Book Trend Prediction
arXiv · Oct 16, 2026
Physics-informed diffusion models in spectral space
arXiv · Jun 3, 2026