Differentially Private Bayesian Inference for Generalized Linear Models

TL;DR

This paper introduces a privacy-preserving Bayesian inference method for generalized linear models, enabling uncertainty quantification under differential privacy constraints, demonstrated with logistic and Poisson regressions.

Contribution

It presents a novel noise-aware DP Bayesian inference approach for GLMs that quantifies parameter uncertainty while maintaining strong privacy guarantees.

Findings

Posteriors are close to non-private counterparts.

Method provides statistically significant coefficient identification.

Achieves tight privacy analysis.

Abstract

Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst's repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy (DP) constraints provide only private point estimates of the regression coefficients, and are not able to quantify parameter uncertainty. In this work, with logistic and Poisson regression as running examples, we introduce a generic noise-aware DP Bayesian inference method for a GLM at hand, given a noisy sum of summary statistics. Quantifying uncertainty allows us to determine which of the regression coefficients are statistically significantly different from zero. We provide a previously unknown tight privacy analysis and experimentally demonstrate that the posteriors obtained from our model, while adhering to strong privacy guarantees, are close to the non-private posteriors.