Differentially private methods for managing model uncertainty in linear\n regression models

2021/09/08 by Víctor Peña, Peña, Víctor, Andrés F. Barrientos +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Privacy-Preserving Technologies in Data #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials

paper · pdf · doi:10.48550/arxiv.2109.03949

openalex publication_date 2021/09/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Revisiting Differentially Private Hypothesis Tests for Categorical Data
• Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso
• Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising
• Differentially Private Bayesian Linear Regression

Related

• Differentially Private Bayesian Linear Regression
• Differentially Private Model Selection with Penalized and Constrained Likelihood
• Differentially Private Bayesian Inference for Generalized Linear Models
• Hypothesis Testing for Differentially Private Linear Regression
• Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain