  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.
