Differentially Private Bayesian Inference for Generalized Linear Models

• URL: http://arxiv.org/abs/2011.00467v3
• Date: Wed, 12 May 2021 08:57:39 GMT
• Title: Differentially Private Bayesian Inference for Generalized Linear Models
• Authors: Tejas Kulkarni, Joonas J\"alk\"o, Antti Koskela, Samuel Kaski and Antti Honkela
• Abstract summary: Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst's repertoire. We introduce a generic noise-aware DP Bayesian inference method for a GLM, given a noisy sum of summary statistics. We experimentally demonstrate that the posteriors obtained from our model, while adhering to strong privacy guarantees, are close to the non-private posteriors.
• Score: 21.942149563564968
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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