IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v77y2014icp313-325.html
   My bibliography  Save this article

Nonparametric additive model with grouped lasso and maximizing area under the ROC curve

Author

Listed:
  • Choi, Sungwoo
  • Park, Junyong

Abstract

An ROC (Receiver Operating Characteristic) curve is a popular tool in the classification of two populations. The nonparametric additive model is used to construct a classifier which is estimated by maximizing the U-statistic type of empirical AUC (Area Under Curve). In particular, the sparsity situation is considered in the sense that only a small number of variables is significant in the classification, so it is demanded that lots of noisy variables will be removed. Some theoretical result on the necessity of variable selection under the sparsity condition is provided since the AUC of the classifier from maximization of empirical AUC is not guaranteed to be optimal. To select significant variables in the classification, the grouped lasso which has been widely used when groups of parameters need to be either selected or discarded simultaneously is used. In addition, the performance of the proposed method is evaluated by numerical studies including simulation and real data examples compared with other existing approaches.

Suggested Citation

  • Choi, Sungwoo & Park, Junyong, 2014. "Nonparametric additive model with grouped lasso and maximizing area under the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 313-325.
    • Handle: RePEc:eee:csdana:v:77:y:2014:i:c:p:313-325
    DOI: 10.1016/j.csda.2014.03.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314000875
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.03.010?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. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    2. Margaret Sullivan Pepe & Tianxi Cai & Gary Longton, 2006. "Combining Predictors for Classification Using the Area under the Receiver Operating Characteristic Curve," Biometrics, The International Biometric Society, vol. 62(1), pages 221-229, March.
    3. 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.
    4. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
    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. Pedro Delicado & Philippe Vieu, 2017. "Choosing the most relevant level sets for depicting a sample of densities," Computational Statistics, Springer, vol. 32(3), pages 1083-1113, September.

    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. Ye, Ya-Fen & Shao, Yuan-Hai & Deng, Nai-Yang & Li, Chun-Na & Hua, Xiang-Yu, 2017. "Robust Lp-norm least squares support vector regression with feature selection," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 32-52.
    3. Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    4. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    5. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    6. Jiang, Cuixia & Xiong, Wei & Xu, Qifa & Liu, Yezheng, 2021. "Predicting default of listed companies in mainland China via U-MIDAS Logit model with group lasso penalty," Finance Research Letters, Elsevier, vol. 38(C).
    7. Osamu Komori & Shinto Eguchi & John B. Copas, 2015. "Generalized t-statistic for two-group classification," Biometrics, The International Biometric Society, vol. 71(2), pages 404-416, June.
    8. Wei, Fengrong & Zhu, Hongxiao, 2012. "Group coordinate descent algorithms for nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 316-326.
    9. Luu, Tung Duy & Fadili, Jalal & Chesneau, Christophe, 2019. "PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 209-233.
    10. Zeng, Yaohui & Yang, Tianbao & Breheny, Patrick, 2021. "Hybrid safe–strong rules for efficient optimization in lasso-type problems," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    11. Lee, In Gyu & Yoon, Sang Won & Won, Daehan, 2022. "A Mixed Integer Linear Programming Support Vector Machine for Cost-Effective Group Feature Selection: Branch-Cut-and-Price Approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1055-1068.
    12. Ruidi Chen & Ioannis Ch. Paschalidis, 2022. "Robust Grouped Variable Selection Using Distributionally Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1042-1071, September.
    13. Sophie Lambert-Lacroix & Laurent Zwald, 2016. "The adaptive BerHu penalty in robust regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 487-514, September.
    14. 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.
    15. A. Karagrigoriou & C. Koukouvinos & K. Mylona, 2010. "On the advantages of the non-concave penalized likelihood model selection method with minimum prediction errors in large-scale medical studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 13-24.
    16. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.
    17. Shota Yamanaka & Nobuo Yamashita, 2018. "Duality of nonconvex optimization with positively homogeneous functions," Computational Optimization and Applications, Springer, vol. 71(2), pages 435-456, November.
    18. Chen, Ying & Niu, Linlin & Chen, Ray-Bing & He, Qiang, 2019. "Sparse-Group Independent Component Analysis with application to yield curves prediction," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 76-89.
    19. Lichun Wang & Yuan You & Heng Lian, 2015. "Convergence and sparsity of Lasso and group Lasso in high-dimensional generalized linear models," Statistical Papers, Springer, vol. 56(3), pages 819-828, August.
    20. 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.

    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:77:y:2014:i:c:p:313-325. 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.