Reviews: Differentially Private Bayesian Inference for Exponential Families

This paper proposes an approach for differentially private estimation of the posterior distribution in conjugate exponential-family models. Similar to previous "naive" approaches, it enforces privacy by adding Laplace-distributed noise to the sufficient statistic. Where a naive approach would treat this noisy statistic as true, the main contribution of this paper is a Gibbs sampling algorithm to integrate over uncertainty in the true statistic given the observed noisy statistic. This is the proper Bayesian procedure, and the experiments show that this yields better-calibrated posterior estimates than naive updating or one-posterior sampling (OPS). The paper is very clear, cleanly written and easy to follow; I found no obvious mistakes.