# Differentially Private Bayesian Inference for Generalized Linear Models

arXiv: https://arxiv.org/abs/2011.00467 · HTML: https://mlsanity.com/paper/2011.00467/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2020.

## Built on by (most cited first, 16 of 16)

- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Differentially Private Regression with Unbounded Covariates](https://mlsanity.com/paper/2202.11199/) (2022)
- [Incentives in Private Collaborative Machine Learning](https://mlsanity.com/paper/2404.01676/) (2024)
- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability](https://mlsanity.com/paper/2107.08461/) (2021)
- [Gaussian DP for Reporting Differential Privacy Guarantees in Machine Learning](https://mlsanity.com/paper/2503.10945/) (2025)
- [Private Regression via Data-Dependent Sufficient Statistic Perturbation](https://mlsanity.com/paper/2405.15002/) (2024)
- [Gaussian Processes with Differential Privacy](https://mlsanity.com/paper/2106.00474/) (2021)
- [Sharper Utility Bounds for Differentially Private Models](https://mlsanity.com/paper/2204.10536/) (2022)
- [DPVIm: Differentially Private Variational Inference Improved](https://mlsanity.com/paper/2210.15961/) (2022)
- [Locally Differentially Private Bayesian Inference](https://mlsanity.com/paper/2110.14426/) (2021)
- [Differentially private stochastic expectation propagation (DP-SEP)](https://mlsanity.com/paper/2111.13219/) (2021)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [Simulation-based Bayesian Inference from Privacy Protected Data](https://mlsanity.com/paper/2310.12781/) (2023)
- [Noise-Aware Differentially Private Variational Inference](https://mlsanity.com/paper/2410.19371/) (2024)
- [Optimal Survey Design for Private Mean Estimation](https://mlsanity.com/paper/2501.18121/) (2025)

## Abstract (arXiv)

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.