Differentially Private Bayesian Inference for Generalized Linear Models
Tejas Kulkarni,u00a0Joonas Ju00e4lku00f6,u00a0Antti Koskela,u00a0Samuel Kaski,u00a0Antti Honkela
Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analystu2019s 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.
