IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v23y2011i1p185-199.html
   My bibliography  Save this article

An ordinary differential equation-based solution path algorithm

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2010.490584
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2010.490584?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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    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.

    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. T. Cai & J. Huang & L. Tian, 2009. "Regularized Estimation for the Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(2), pages 394-404, June.
    2. Heng Lian & Xin Chen & Jian-Yi Yang, 2012. "Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences," Biometrics, The International Biometric Society, vol. 68(2), pages 437-445, June.
    3. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    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.
    5. Young Joo Yoon & Cheolwoo Park & Erik Hofmeister & Sangwook Kang, 2012. "Group variable selection in cardiopulmonary cerebral resuscitation data for veterinary patients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1605-1621, January.
    6. 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.
    7. Engler David & Li Yi, 2009. "Survival Analysis with High-Dimensional Covariates: An Application in Microarray Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-22, February.
    8. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    9. Belli, Edoardo, 2022. "Smoothly adaptively centered ridge estimator," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    10. Alena Skolkova, 2023. "Instrumental Variable Estimation with Many Instruments Using Elastic-Net IV," CERGE-EI Working Papers wp759, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    11. Wei Sun & Lexin Li, 2012. "Multiple Loci Mapping via Model-free Variable Selection," Biometrics, The International Biometric Society, vol. 68(1), pages 12-22, March.
    12. Zhixuan Fu & Chirag R. Parikh & Bingqing Zhou, 2017. "Penalized variable selection in competing risks regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 353-376, July.
    13. Ke Yu & Shan Luo, 2022. "A sequential feature selection procedure for high-dimensional Cox proportional hazards model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1109-1142, December.
    14. 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.
    15. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    16. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    17. Gareth M. James & Peter Radchenko & Jinchi Lv, 2009. "DASSO: connections between the Dantzig selector and lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 127-142, January.
    18. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    19. Camila Epprecht & Dominique Guegan & Álvaro Veiga & Joel Correa da Rosa, 2017. "Variable selection and forecasting via automated methods for linear models: LASSO/adaLASSO and Autometrics," Post-Print halshs-00917797, HAL.
    20. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.

    More about this item

    Statistics

    Access and download statistics

    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:taf:gnstxx:v:23:y:2011:i:1:p:185-199. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.