Differentially Private Markov Chain Monte Carlo
This work addresses privacy-preserving Bayesian inference for data subjects, offering a novel method that overcomes previous limitations in DP MCMC.
The authors tackled the challenge of performing differentially private Bayesian learning without unrealistic assumptions on Markov chain convergence, presenting the first general DP Markov chain Monte Carlo algorithm applicable to arbitrary models. They achieved this by decomposing the Barker acceptance test to evaluate Rényi DP privacy costs and improved guarantees through data subsampling and approximate tests.
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 Rényi DP privacy cost of the accept-reject choice. We further show how to improve the DP guarantee through data subsampling and approximate acceptance tests.