# R'enyi Differential Privacy Mechanisms for Posterior Sampling

arXiv: https://arxiv.org/abs/1710.00892 · HTML: https://mlsanity.com/paper/1710.00892/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2017.

## Built on by (most cited first, 16 of 16)

- [Submix: Practical Private Prediction for Large-Scale Language Models](https://mlsanity.com/paper/2201.00971/) (2022)
- [Incentives in Private Collaborative Machine Learning](https://mlsanity.com/paper/2404.01676/) (2024)
- [The Saddle-Point Accountant for Differential Privacy](https://mlsanity.com/paper/2208.09595/) (2022)
- [Learning-Augmented Private Algorithms for Multiple Quantile Release](https://mlsanity.com/paper/2210.11222/) (2022)
- [Privacy Amplification Via Bernoulli Sampling](https://mlsanity.com/paper/2105.10594/) (2021)
- [Tractable MCMC for Private Learning with Pure and Gaussian Differential Privacy](https://mlsanity.com/paper/2310.14661/) (2023)
- [Dirichlet Mechanism for Differentially Private KL Divergence Minimization](https://mlsanity.com/paper/2110.01984/) (2021)
- [Can Stochastic Gradient Langevin Dynamics Provide Differential Privacy for Deep Learning?](https://mlsanity.com/paper/2110.05057/) (2021)
- [Differentially private partitioned variational inference](https://mlsanity.com/paper/2209.11595/) (2022)
- [Differential Privacy for Transformer Embeddings of Text with Nonparametric Variational Information Bottleneck](https://mlsanity.com/paper/2601.02307/) (2026)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [Universally Harmonizing Differential Privacy Mechanisms for Federated Learning: Boosting Accuracy and Convergence](https://mlsanity.com/paper/2407.14710/) (2024)
- [Computation-Utility-Privacy Tradeoffs in Bayesian Estimation](https://mlsanity.com/paper/2603.18254/) (2026)
- [Differential privacy guarantees of Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/2502.17150/) (2025)
- [Differential Privacy of Gaussian Process Posterior Sampling](https://mlsanity.com/paper/2606.17995/) (2026)
- [On Inherent Privacy of Posterior Sampling: A Unified R'enyi-Divergence Framework](https://mlsanity.com/paper/2610.19573/) (2026)

## Abstract (arXiv)

Using a recently proposed privacy definition of R'enyi Differential Privacy (RDP), we re-examine the inherent privacy of releasing a single sample from a posterior distribution. We exploit the impact of the prior distribution in mitigating the influence of individual data points. In particular, we focus on sampling from an exponential family and specific generalized linear models, such as logistic regression. We propose novel RDP mechanisms as well as offering a new RDP analysis for an existing method in order to add value to the RDP framework. Each method is capable of achieving arbitrary RDP privacy guarantees, and we offer experimental results of their efficacy.