DP-SEP: Differentially private stochastic expectation propagation

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. However, using EP for large-scale datasets imposes a challenge in terms of memory requirements as it needs to maintain each of the local approximates in memory. To overcome this problem, stochastic expectation propagation (SEP) was proposed, which only considers a unique local factor that captures the average effect of each likelihood term to the posterior and refines it in a way analogous to EP. Therefore in this work, we focus on developing a differentially private stochastic expectation propagation(DP-SEP) algorithm, which outputs differentially private natural parameters of the exponential-family posteriors in each step of SEP.