Ziliang Shen

Caixing Wang, Ziliang Shen

In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and data heterogeneity. However, the non-smoothness of the check loss function poses big challenges to both computation and theory in the distributed setting. To tackle these problems, we transform the original quantile regression into the least-squares optimization. By applying a double-smoothing approach, we extend a previous Newton-type distributed approach without the restrictive independent assumption between the error term and covariates. An efficient algorithm is developed, which enjoys high computation and communication efficiency. Theoretically, the proposed distributed estimator achieves a near-oracle convergence rate and high support recovery accuracy after a constant number of iterations. Extensive experiments on synthetic examples and a real data application further demonstrate the effectiveness of the proposed method.

Ziliang Shen, Caixing Wang, Shaoli Wang et al.

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.