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Communication-efficient distributed estimation for high-dimensional large-scale linear regression

Author

Listed:
  • Zhan Liu

    (Hubei University)

  • Xiaoluo Zhao

    (Hubei University)

  • Yingli Pan

    (Hubei University)

Abstract

In the Master-Worker distributed structure, this paper provides a regularized gradient-enhanced loss (GEL) function based on the high-dimensional large-scale linear regression with SCAD and adaptive LASSO penalty. The importance and originality of this paper have two aspects: (1) Computationally, to take full advantage of the computing power of each machine and speed up the convergence, our proposed distributed upgraded estimation method can make all Workers optimize their corresponding GEL functions in parallel, and the results are then aggregated by the Master; (2) In terms of communication, the proposed modified proximal alternating direction method of the multipliers (ADMM) algorithm is comparable to the Centralize method based on the full sample during a few rounds of communication. Under some mild assumptions, we establish the Oracle properties of the SCAD and adaptive LASSO penalized linear regression. The finite sample properties of the newly suggested method are assessed through simulation studies. An application to the HIV drug susceptibility study demonstrates the utility of the proposed method in practice.

Suggested Citation

  • Zhan Liu & Xiaoluo Zhao & Yingli Pan, 2023. "Communication-efficient distributed estimation for high-dimensional large-scale linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 455-485, May.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:4:d:10.1007_s00184-022-00878-x
    DOI: 10.1007/s00184-022-00878-x
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Michael I. Jordan & Jason D. Lee & Yun Yang, 2019. "Communication-Efficient Distributed Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 668-681, April.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Aijun Hu & Chujin Li & Jing Wu & Roberto Natella, 2021. "Communication-Efficient Modeling with Penalized Quantile Regression for Distributed Data," Complexity, Hindawi, vol. 2021, pages 1-16, January.
    5. Huixia Judy Wang & Ian W. McKeague & Min Qian, 2018. "Testing for marginal linear effects in quantile regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 433-452, March.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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