B0425
Title: Feature-splitting algorithms for ultrahigh dimensional quantile regression
Authors: Runze Li - The Pennsylvania State University (United States) [presenting]
Jiawei Wen - Meta Platforms Inc (United States)
Songshan Yang - Renmin University of China (China)
Christina Dan Wang - NYU Shanghai (China)
Yifan Jiang - Pennsylvania State University (United States)
Abstract: The concern is the computational issues related to penalized quantile regression (PQR) with ultrahigh dimensional predictors. Various algorithms have been developed for PQR, but they become ineffective and/or infeasible in the presence of ultrahigh dimensional predictors due to storage and scalability limitations. The variable updating schema of the feature-splitting algorithm that directly applies the ordinary alternating direction method of multiplier (ADMM) to ultrahigh dimensional PQR may make the algorithm fail to converge. To tackle this hurdle, an efficient and parallelizable algorithm is proposed for ultrahigh dimensional PQR based on the three-block ADMM. The compatibility of the proposed algorithm with parallel computing alleviates the storage and scalability limitations of a single machine in large-scale data processing. The rate of convergence of the newly proposed algorithm is established. In addition, Monte Carlo simulations are conducted to compare the finite sample performance of the proposed algorithm with that of other existing algorithms. The numerical comparison implies that the proposed algorithm significantly outperforms the existing ones. The proposed algorithm is further illustrated via an empirical analysis of a real-world data set.
