Differentially Private Stochastic Expectation Propagation

Published: 24 Oct 2022, Last Modified: 28 Feb 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: We are interested in privatizing an approximate posterior inference algorithm, called Expectation Propagation (EP). EP approximates the posterior distribution by iteratively refining approximations to the local likelihood terms. By doing so, EP typically provides better posterior uncertainties than variational inference (VI) which globally approximates the likelihood term. However, EP needs a large memory to maintain all local approximations 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 privatization, SEP is more tractable than EP. It is because at each factor’s refining step we fix the remaining factors, where these factors are independent of other datapoints, which is different from EP. This independence makes the sensitivity analysis straightforward. We provide a theoretical analysis of the privacy-accuracy trade-off in the posterior distributions under our method, which we call differentially private stochastic expectation propagation (DP-SEP). Furthermore, we test the DP-SEP algorithm on both synthetic and real-world datasets and evaluate the quality of posterior estimates at different levels of guaranteed privacy.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=Gjt07VwAqP&noteId=wE9fIwT9XB
Changes Since Last Submission: Code repository anonymized accordingly to the past submission recommendation
Assigned Action Editor: ~Yu-Xiang_Wang1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 165