Differentially private methods for managing model uncertainty in linear regression models

TL;DR

This paper introduces differentially private techniques for hypothesis testing, model averaging, and selection in linear regression, ensuring privacy while maintaining statistical validity and practical implementation.

Contribution

It develops both Bayesian and non-Bayesian methods for private inference in linear models, addressing practical issues like error rates and uncertainty quantification.

Findings

Procedures are asymptotically consistent.

Methods are straightforward to implement with existing software.

Adjustments ensure proper type I error control.

Abstract

In this work, we propose differentially private methods for hypothesis testing, model averaging, and model selection for normal linear models. We consider Bayesian methods based on mixtures of $g$-priors and non-Bayesian methods based on likelihood-ratio statistics and information criteria. The procedures are asymptotically consistent and straightforward to implement with existing software. We focus on practical issues such as adjusting critical values so that hypothesis tests have adequate type I error rates and quantifying the uncertainty introduced by the privacy-ensuring mechanisms.