# Differentially Private Estimation and Inference in High-Dimensional Regression with FDR Control

arXiv: https://arxiv.org/abs/2310.16260 · HTML: https://mlsanity.com/paper/2310.16260/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2023.

## Built on by (most cited first, 4 of 4)

- [Better Locally Private Sparse Estimation Given Multiple Samples Per User](https://mlsanity.com/paper/2408.04313/) (2024)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm](https://mlsanity.com/paper/2401.08150/) (2024)
- [Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule](https://mlsanity.com/paper/2602.12604/) (2026)

## Abstract (arXiv)

This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the unknown sparsity parameter in differentially private sparse linear regression (DP-SLR), eliminating the need for prior knowledge of model sparsity, which is a requisite in the existing literature. Next, we develop the DP debiased algorithm that enables privacy-preserving inference on a particular subset of regression parameters. Our proposed method enables privacy-preserving inference on the regression parameters by leveraging the inherent sparsity of high-dimensional linear regression models. Additionally, we address private feature selection by considering multiple testing in high-dimensional linear regression by introducing a DP multiple testing procedure that controls the false discovery rate (FDR). This allows for accurate and privacy-preserving identification of significant predictors in the regression model. Through extensive simulations and real data analyses, we demonstrate the effectiveness of our proposed methods in conducting inference for high-dimensional linear models while safeguarding privacy and controlling the FDR.