Differentially private methods for managing model uncertainty in linear regression models

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.

References in corpus (5)

• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• Criteria for Bayesian model choice with application to variable selection
• Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso
• Privacy-preserving parametric inference: a case for robust statistics
• Differentially Private Bayesian Linear Regression

Cited by in corpus (1)

• Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy