High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference

• URL: http://arxiv.org/abs/2508.05212v1
• Date: Thu, 07 Aug 2025 09:47:44 GMT
• Title: High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference
• Authors: Ziliang Shen, Caixing Wang, Shaoli Wang, Yibo Yan,
• Abstract summary: We propose a differentially private quantile regression method for high-dimensional data in a distributed setting.<n>We develop a differentially private estimation algorithm with iterative updates, ensuring near-optimal statistical accuracy and formal privacy guarantees.
• Score: 0.26784722398800515
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With the development of big data and machine learning, privacy concerns have become increasingly critical, especially when handling heterogeneous datasets containing sensitive personal information. Differential privacy provides a rigorous framework for safeguarding individual privacy while enabling meaningful statistical analysis. In this paper, we propose a differentially private quantile regression method for high-dimensional data in a distributed setting. Quantile regression is a powerful and robust tool for modeling the relationships between the covariates and responses in the presence of outliers or heavy-tailed distributions. To address the computational challenges due to the non-smoothness of the quantile loss function, we introduce a Newton-type transformation that reformulates the quantile regression task into an ordinary least squares problem. Building on this, we develop a differentially private estimation algorithm with iterative updates, ensuring both near-optimal statistical accuracy and formal privacy guarantees. For inference, we further propose a differentially private debiased estimator, which enables valid confidence interval construction and hypothesis testing. Additionally, we propose a communication-efficient and differentially private bootstrap for simultaneous hypothesis testing in high-dimensional quantile regression, suitable for distributed settings with both small and abundant local data. Extensive simulations demonstrate the robustness and effectiveness of our methods in practical scenarios.

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