Differentially Private Bayesian Inference for Exponential Families

TL;DR

This paper introduces a novel method for performing Bayesian inference on exponential family models that ensures differential privacy while accurately accounting for privacy-induced noise, providing reliable posterior estimates even with limited data.

Contribution

It presents the first approach for private Bayesian inference in exponential families that properly calibrates posterior beliefs considering privacy noise, using only sufficient statistics.

Findings

Provides properly calibrated posterior beliefs under differential privacy.

Efficiently uses sufficient statistics, avoiding individual data processing.

Works effectively in non-asymptotic data regimes.

Abstract

The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it works only with sufficient statistics and not individual data. Unlike other methods, it gives properly calibrated posterior beliefs in the non-asymptotic data regime.