# Differentially Private Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/1901.10275 · HTML: https://mlsanity.com/paper/1901.10275/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2019.

## Built on by (most cited first, 18 of 18)

- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability](https://mlsanity.com/paper/2107.08461/) (2021)
- [Protect Your Score: Contact Tracing With Differential Privacy Guarantees](https://mlsanity.com/paper/2312.11581/) (2023)
- [Gaussian Processes with Differential Privacy](https://mlsanity.com/paper/2106.00474/) (2021)
- [Statistic Selection and MCMC for Differentially Private Bayesian Estimation](https://mlsanity.com/paper/2203.13377/) (2022)
- [Sharper Utility Bounds for Differentially Private Models](https://mlsanity.com/paper/2204.10536/) (2022)
- [DP-Fast MH: Private, Fast, and Accurate Metropolis-Hastings for Large-Scale Bayesian Inference](https://mlsanity.com/paper/2303.06171/) (2023)
- [Differentially private partitioned variational inference](https://mlsanity.com/paper/2209.11595/) (2022)
- [Locally Differentially Private Bayesian Inference](https://mlsanity.com/paper/2110.14426/) (2021)
- [Differentially Private Online Bayesian Estimation With Adaptive Truncation](https://mlsanity.com/paper/2301.08202/) (2023)
- [Differentially Private Distributed Bayesian Linear Regression with MCMC](https://mlsanity.com/paper/2301.13778/) (2023)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [Differentially private Bayesian tests](https://mlsanity.com/paper/2401.15502/) (2024)
- [Robust One Round Federated Learning with Predictive Space Bayesian Inference](https://mlsanity.com/paper/2206.09526/) (2022)
- [Noise-Aware Differentially Private Variational Inference](https://mlsanity.com/paper/2410.19371/) (2024)
- [Federated and differentially private estimation of KL divergence](https://mlsanity.com/paper/2411.16478/) (2024)
- [Differential privacy guarantees of Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/2502.17150/) (2025)
- [Differentially Private Geodesic Regression](https://mlsanity.com/paper/2504.11304/) (2025)

## Abstract (arXiv)

Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC) algorithm whose privacy-guarantees are not subject to unrealistic assumptions on Markov chain convergence and that is applicable to posterior inference in arbitrary models. Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the R'enyi DP privacy cost of the accept-reject choice. We further show how to improve the DP guarantee through data subsampling and approximate acceptance tests.