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Feature-splitting Algorithms for Ultrahigh Dimensional Quantile Regression.

Jiawei Wen1, Songshan Yang2, Christina Dan Wang3

  • 1Meta Platforms Inc., 1 Hacker Way, Menlo Park, CA 94025, USA.

Journal of Econometrics
|August 8, 2025
PubMed
Summary
This summary is machine-generated.

We developed a new three-block ADMM algorithm for ultrahigh dimensional penalized quantile regression (PQR). This efficient, parallelizable method overcomes storage and scalability issues, outperforming existing algorithms in simulations and real-world data analysis.

Keywords:
ADMMParallel computingPenalized quantile regressionSample-splitting algorithm

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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.