Feature-splitting Algorithms for Ultrahigh Dimensional Quantile Regression

Area of Science:

• Computational Statistics
• High-Dimensional Data Analysis

Background:

• Penalized quantile regression (PQR) faces computational challenges with ultrahigh dimensional predictors.
• Existing algorithms struggle with storage and scalability in high dimensions.
• Standard alternating direction method of multipliers (ADMM) may fail to converge for PQR in ultrahigh dimensions.

Purpose of the Study:

• To propose an efficient and parallelizable algorithm for ultrahigh dimensional PQR.
• To address the convergence and scalability limitations of existing methods.
• To establish the theoretical convergence rate of the new algorithm.

Main Methods:

• Development of a novel three-block ADMM algorithm tailored for ultrahigh dimensional PQR.
• Leveraging parallel computing capabilities to overcome single-machine limitations.
• Theoretical analysis to establish the algorithm's convergence rate.

Main Results:

• The proposed three-block ADMM algorithm demonstrates efficiency and parallelizability.
• The algorithm effectively handles storage and scalability limitations in large-scale datasets.
• Monte Carlo simulations show superior performance compared to existing PQR algorithms.
• Convergence rate of the new algorithm is theoretically established.

Conclusions:

• The proposed three-block ADMM algorithm offers a robust solution for ultrahigh dimensional PQR.
• Parallel computing compatibility enhances its applicability to big data problems.
• Empirical results confirm its significant advantages over current methods.