IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v203y2025ics0167947324001658.html
   My bibliography  Save this article

A unified consensus-based parallel algorithm for high-dimensional regression with combined regularizations

Author

Listed:
  • Wu, Xiaofei
  • Liang, Rongmei
  • Zhang, Zhimin
  • Cui, Zhenyu

Abstract

The parallel algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical learning models. However, there is currently limited research on parallel algorithms specifically designed for high-dimensional regression with combined regularization terms. These terms, such as elastic-net, sparse group lasso, sparse fused lasso, and their nonconvex variants, have gained significant attention in various fields due to their ability to incorporate prior information and promote sparsity within specific groups or fused variables. The scarcity of parallel algorithms for combined regularizations can be attributed to the inherent nonsmoothness and complexity of these terms, as well as the absence of closed-form solutions for certain proximal operators associated with them. This paper proposes a unified constrained optimization formulation based on the consensus problem for these types of convex and nonconvex regression problems, and derives the corresponding parallel alternating direction method of multipliers (ADMM) algorithms. Furthermore, it is proven that the proposed algorithm not only has global convergence but also exhibits a linear convergence rate. It is worth noting that the computational complexity of the proposed algorithm remains the same for different regularization terms and losses, which implicitly demonstrates the universality of this algorithm. Extensive simulation experiments, along with a financial example, serve to demonstrate the reliability, stability, and scalability of our algorithm. The R package for implementing the proposed algorithm can be obtained at https://github.com/xfwu1016/CPADMM.

Suggested Citation

  • Wu, Xiaofei & Liang, Rongmei & Zhang, Zhimin & Cui, Zhenyu, 2025. "A unified consensus-based parallel algorithm for high-dimensional regression with combined regularizations," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:csdana:v:203:y:2025:i:c:s0167947324001658
    DOI: 10.1016/j.csda.2024.108081
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001658
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108081?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Joki, Kaisa & Bagirov, Adil M. & Karmitsa, Napsu & Mäkelä, Marko M. & Taheri, Sona, 2020. "Clusterwise support vector linear regression," European Journal of Operational Research, Elsevier, vol. 287(1), pages 19-35.
    3. Wu, Xiaofei & Ming, Hao & Zhang, Zhimin & Cui, Zhenyu, 2024. "Multi-block alternating direction method of multipliers for ultrahigh dimensional quantile fused regression," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    4. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    5. Liao, Zhiqiang & Dai, Sheng & Kuosmanen, Timo, 2024. "Convex support vector regression," European Journal of Operational Research, Elsevier, vol. 313(3), pages 858-870.
    6. Qin, Shanshan & Wu, Yuehua, 2020. "General matching quantiles M-estimation," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    7. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    8. 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.
    9. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    10. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    11. Xiu, Xianchao & Liu, Wanquan & Li, Ling & Kong, Lingchen, 2019. "Alternating direction method of multipliers for nonconvex fused regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 59-71.
    12. Sgouropoulos, Nikolaos & Yao, Qiwei & Yastremiz, Claudia, 2015. "Matching a distribution by matching quantiles estimation," LSE Research Online Documents on Economics 57221, London School of Economics and Political Science, LSE Library.
    13. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    14. Fu, Saiji & Tian, Yingjie & Tang, Long, 2023. "Robust regression under the general framework of bounded loss functions," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1325-1339.
    15. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    16. Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.
    17. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    18. Nikolaos Sgouropoulos & Qiwei Yao & Claudia Yastremiz, 2015. "Matching a Distribution by Matching Quantiles Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 742-759, June.
    19. Wang, Xiaoming & Park, Taesung & Carriere, K.C., 2010. "Variable selection via combined penalization for high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2230-2243, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    2. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    3. Zanhua Yin, 2020. "Variable selection for sparse logistic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 821-836, October.
    4. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    5. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    6. Siwei Xia & Yuehan Yang & Hu Yang, 2022. "Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 255-277, March.
    7. Ismail Shah & Hina Naz & Sajid Ali & Amani Almohaimeed & Showkat Ahmad Lone, 2023. "A New Quantile-Based Approach for LASSO Estimation," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    8. T. Tony Cai & Zijian Guo & Yin Xia, 2023. "Statistical inference and large-scale multiple testing for high-dimensional regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1135-1171, December.
    9. Shanshan Qin & Hao Ding & Yuehua Wu & Feng Liu, 2021. "High-dimensional sign-constrained feature selection and grouping," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 787-819, August.
    10. Laura Freijeiro‐González & Manuel Febrero‐Bande & Wenceslao González‐Manteiga, 2022. "A Critical Review of LASSO and Its Derivatives for Variable Selection Under Dependence Among Covariates," International Statistical Review, International Statistical Institute, vol. 90(1), pages 118-145, April.
    11. Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    12. Tomáš Plíhal, 2021. "Scheduled macroeconomic news announcements and Forex volatility forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1379-1397, December.
    13. Victor Chernozhukov & Christian Hansen & Yuan Liao, 2015. "A lava attack on the recovery of sums of dense and sparse signals," CeMMAP working papers CWP56/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    15. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.
    16. Fang, Xiaolei & Paynabar, Kamran & Gebraeel, Nagi, 2017. "Multistream sensor fusion-based prognostics model for systems with single failure modes," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 322-331.
    17. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
    18. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    19. Kwon, Sunghoon & Oh, Seungyoung & Lee, Youngjo, 2016. "The use of random-effect models for high-dimensional variable selection problems," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 401-412.
    20. Howard D. Bondell & Brian J. Reich, 2009. "Simultaneous Factor Selection and Collapsing Levels in ANOVA," Biometrics, The International Biometric Society, vol. 65(1), pages 169-177, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:203:y:2025:i:c:s0167947324001658. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.