Bayesian Inference Under Differential Privacy With Bounded Data

2024/05/22 by Kazan, Zeki, Reiter, Jerome P.
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2405.13801

Abstract

We describe Bayesian inference for the parameters of Gaussian models of bounded data protected by differential privacy. Using this setting, we demonstrate that analysts can and should take constraints imposed by the bounds into account when specifying prior distributions. Additionally, we provide theoretical and empirical results regarding what classes of default priors produce valid inference for a differentially private release in settings where substantial prior information is not available. We discuss how these results can be applied to Bayesian inference for regression with differentially private data.

Related

• On the Differential Privacy of Bayesian Inference
• Bayesian Differential Privacy through Posterior Sampling
• Differentially Private Bayesian Linear Regression
• Privacy Guarantees in Posterior Sampling under Contamination
• Differentially Private Model Selection with Penalized and Constrained Likelihood