Differentially Private Bayesian Linear Regression

Abstract

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mechanism does a poor job in realistic data settings. We then develop noise-aware methods that perform inference over the privacy mechanism and produce correct posteriors across a wide range of scenarios.

NeurIPS 2019

Cited by in corpus (9)

• Parametric Bootstrap for Differentially Private Confidence Intervals
• Input Perturbation: A New Paradigm between Central and Local Differential Privacy
• Weighted Distributed Differential Privacy ERM: Convex and Non-convex
• Fair Decision Making using Privacy-Protected Data
• Differentially private methods for managing model uncertainty in linear regression models
• Differentially Private Bayesian Inference for Generalized Linear Models
• Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability
• Locally Differentially Private Bayesian Inference
• Gaussian Processes with Differential Privacy