Bayesian Inference Under Differential Privacy With Bounded Data

TL;DR

This paper develops Bayesian inference methods for Gaussian models with bounded data under differential privacy, emphasizing the importance of prior constraints and analyzing default priors for valid inference in privacy-preserving settings.

Contribution

It introduces a framework for Bayesian inference with bounded data under differential privacy, highlighting the role of prior constraints and evaluating default priors for privacy-preserving analysis.

Findings

Prior constraints improve inference accuracy under differential privacy.

Certain default priors can produce valid Bayesian inference in private settings.

The methods are applicable to differentially private regression analysis.

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.