On the Differential Privacy of Bayesian Inference
This work addresses privacy concerns in Bayesian analysis for data scientists and statisticians, representing an incremental advancement in differential privacy methods.
The paper tackles the problem of communicating Bayesian inference results while preserving differential privacy, presenting four algorithms for private Bayesian inference on probabilistic graphical models with utility and privacy bounds.
We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesian updates, either directly to the posterior parameters, or to their Fourier transform so as to preserve update consistency. We also utilise a recently introduced posterior sampling mechanism, for which we prove bounds for the specific but general case of discrete Bayesian networks; and we introduce a maximum-a-posteriori private mechanism. Our analysis includes utility and privacy bounds, with a novel focus on the influence of graph structure on privacy. Worked examples and experiments with Bayesian na{ï}ve Bayes and Bayesian linear regression illustrate the application of our mechanisms.