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

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Cybersecurity & Data Privacy · Depth: Expert, quick

Summary

Zhanrui Cai, Sai Li, Xintao Xia, and Linjun Zhang introduce new methodologies for practical differentially private (DP) estimation and inference in high-dimensional linear regression. Their work, published in 2026, presents a DP Bayesian Information Criterion (DP-BIC) to select unknown sparsity parameters in DP sparse linear regression (DP-SLR), removing the need for prior sparsity knowledge. They also develop a DP debiased algorithm for privacy-preserving inference on specific regression parameters, leveraging the inherent sparsity of high-dimensional models. Additionally, the authors propose a DP multiple testing procedure to control the false discovery rate (FDR) for private feature selection, ensuring accurate identification of significant predictors. Extensive simulations and real data analyses validate the effectiveness of these methods in safeguarding privacy and controlling FDR.

Key takeaway

For data scientists or AI researchers conducting high-dimensional regression analyses with strict privacy requirements, these new differentially private methods offer robust solutions. You can now perform model selection using DP-BIC without needing prior knowledge of model sparsity, conduct privacy-preserving inference on regression parameters, and identify significant features with controlled false discovery rates via DP multiple testing. Consider integrating these techniques to enhance both the privacy guarantees and statistical rigor of your high-dimensional models.

Key insights

New DP methodologies enable robust estimation and inference in high-dimensional regression while controlling FDR.

Principles

• DP-BIC eliminates prior sparsity knowledge.
• DP debiased algorithm enables privacy-preserving inference.
• DP multiple testing controls False Discovery Rate.

Method

Proposes DP-BIC for sparsity selection, a DP debiased algorithm for parameter inference, and a DP multiple testing procedure for FDR-controlled feature selection in high-dimensional linear regression.

In practice

• Selecting unknown sparsity in DP-SLR.
• Privacy-preserving inference on regression parameters.
• Identifying significant predictors with FDR control.

Topics

• Differentially Private Estimation
• High-Dimensional Regression
• False Discovery Rate
• Sparse Linear Regression
• Feature Selection
• Bayesian Information Criterion

Best for: Research Scientist, AI Scientist, Data Scientist, AI Security Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.