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L1‐regularization path algorithm for generalized linear models

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  • Mee Young Park
  • Trevor Hastie

Abstract

Summary. We introduce a path following algorithm for L1‐regularized generalized linear models. The L1‐regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on the L1‐norm of the coefficients, in a manner that is less greedy than forward selection–backward deletion. The generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor–corrector method of convex optimization. Selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths; we suggest intuitive and flexible strategies for choosing appropriate values. We demonstrate the implementation with several simulated and real data sets.

Suggested Citation

  • Mee Young Park & Trevor Hastie, 2007. "L1‐regularization path algorithm for generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 659-677, September.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:659-677
    DOI: 10.1111/j.1467-9868.2007.00607.x
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    2. Baiguo An & Beibei Zhang, 2020. "Logistic regression with image covariates via the combination of L1 and Sobolev regularizations," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-18, June.
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    4. Elena Ivona DUMITRESCU & Sullivan HUE & Christophe HURLIN & Sessi TOKPAVI, 2020. "Machine Learning or Econometrics for Credit Scoring: Let’s Get the Best of Both Worlds," LEO Working Papers / DR LEO 2839, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
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    11. Mao, Xiaojun & Peng, Liuhua & Wang, Zhonglei, 2022. "Nonparametric feature selection by random forests and deep neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    12. Yanis Tazi & Juan E. Arango-Ossa & Yangyu Zhou & Elsa Bernard & Ian Thomas & Amanda Gilkes & Sylvie Freeman & Yoann Pradat & Sean J. Johnson & Robert Hills & Richard Dillon & Max F. Levine & Daniel Le, 2022. "Unified classification and risk-stratification in Acute Myeloid Leukemia," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    13. Dai, Wei & Tsang, Ka Wai, 2023. "A resampling approach for confidence intervals in linear time-series models after model selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    14. Jian Huang & Yuling Jiao & Lican Kang & Jin Liu & Yanyan Liu & Xiliang Lu, 2022. "GSDAR: a fast Newton algorithm for $$\ell _0$$ ℓ 0 regularized generalized linear models with statistical guarantee," Computational Statistics, Springer, vol. 37(1), pages 507-533, March.

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