Differentially private stochastic expectation propagation (DP-SEP)
This work addresses privacy concerns in Bayesian inference for data analysts, but it is incremental as it adapts an existing method (SEP) with differential privacy.
The paper tackles the problem of making approximate posterior inference differentially private by privatizing Stochastic Expectation Propagation (SEP), which is more tractable than standard EP for privacy analysis, and demonstrates the performance of their DP-SEP algorithm on synthetic and real-world datasets with theoretical privacy-accuracy trade-off analysis.
We are interested in privatizing an approximate posterior inference algorithm called Expectation Propagation (EP). EP approximates the posterior by iteratively refining approximations to the local likelihoods, and is known to provide better posterior uncertainties than those by variational inference (VI). However, EP needs a large memory to maintain all local approximates associated with each datapoint in the training data. To overcome this challenge, stochastic expectation propagation (SEP) considers a single unique local factor that captures the average effect of each likelihood term to the posterior and refines it in a way analogous to EP. In terms of privacy, SEP is more tractable than EP because at each refining step of a factor, the remaining factors are fixed and do not depend on other datapoints as in EP, which makes the sensitivity analysis straightforward. We provide a theoretical analysis of the privacy-accuracy trade-off in the posterior estimates under our method, called differentially private stochastic expectation propagation (DP-SEP). Furthermore, we demonstrate the performance of our DP-SEP algorithm evaluated on both synthetic and real-world datasets in terms of the quality of posterior estimates at different levels of guaranteed privacy.