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An ordinary differential equation-based solution path algorithm

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  • Yichao Wu

Abstract

Efron, Hastie, Johnstone, and Tibshirani [(2004), ‘Least Angle Regression (with discussions)’, The Annals of Statistics, 32, 409–499] proposed least angle regression (LAR), a solution path algorithm for the least squares regression. They pointed out that a slight modification of the LAR gives the LASSO [Tibshirani, R. (1996), ‘Regression Shrinkage and Selection Via the Lasso’, Journal of the Royal Statistical Society, Series B, 58, 267–288] solution path. However, it is largely unknown how to extend this solution path algorithm to models beyond the least squares regression. In this work, we propose an extension of the LAR for generalised linear models and the quasi-likelihood model by showing that the corresponding solution path is piecewise given by solutions of ordinary differential equation (ODE) systems. Our contribution is twofold. First, we provide a theoretical understanding on how the corresponding solution path propagates. Second, we propose an ODE-based algorithm to obtain the whole solution path.

Suggested Citation

  • Yichao Wu, 2011. "An ordinary differential equation-based solution path algorithm," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 185-199.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:185-199
    DOI: 10.1080/10485252.2010.490584
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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. Hui Zou, 2008. "A note on path-based variable selection in the penalized proportional hazards model," Biometrika, Biometrika Trust, vol. 95(1), pages 241-247.
    3. Junhui Wang & Xiaotong Shen & Yufeng Liu, 2008. "Probability estimation for large-margin classifiers," Biometrika, Biometrika Trust, vol. 95(1), pages 149-167.
    4. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    5. 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.
    6. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    7. Yuan, Ming & Zou, Hui, 2009. "Efficient Global Approximation of Generalized Nonlinear â„“1-Regularized Solution Paths and Its Applications," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1562-1574.
    8. Ming Yuan & Yi Lin, 2007. "On the non‐negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161, April.
    9. 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.
    10. S. Wu & X. Shen & C. J. Geyer, 2009. "Adaptive regularization using the entire solution surface," Biometrika, Biometrika Trust, vol. 96(3), pages 513-527.
    11. 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.
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    2. Yuan Jiang & Yunxiao He & Heping Zhang, 2016. "Variable Selection With Prior Information for Generalized Linear Models via the Prior LASSO Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 355-376, March.

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