Differentially private stochastic expectation propagation (DP-SEP)

TL;DR

This paper introduces DP-SEP, a differentially private version of stochastic expectation propagation, which efficiently privatizes approximate Bayesian inference with improved privacy-accuracy trade-offs and practical applicability on real datasets.

Contribution

The paper proposes DP-SEP, a novel privacy-preserving algorithm for stochastic expectation propagation, enhancing privacy guarantees while maintaining high-quality posterior estimates.

Findings

DP-SEP achieves favorable privacy-accuracy trade-offs.

The method performs well on synthetic and real datasets.

DP-SEP provides better uncertainty quantification than existing approaches.

Abstract

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.