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Fast sparse regression and classification

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  • Friedman, Jerome H.
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    Abstract

    Many present day applications of statistical learning involve large numbers of predictor variables. Often, that number is much larger than the number of cases or observations available for training the learning algorithm. In such situations, traditional methods fail. Recently, new techniques have been developed, based on regularization, which can often produce accurate models in these settings. This paper describes the basic principles underlying the method of regularization, then focuses on those methods which exploit the sparsity of the predicting model. The potential merits of these methods are then explored by example.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 28 (2012)
    Issue (Month): 3 ()
    Pages: 722-738

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    Handle: RePEc:eee:intfor:v:28:y:2012:i:3:p:722-738

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    Web page: http://www.elsevier.com/locate/ijforecast

    Related research

    Keywords: Regression; Classification; Regularization; Sparsity; Variable selection; Bridge-regression; Lasso; Elastic net; lp-norm penalization;

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    1. Meinshausen, Nicolai, 2007. "Relaxed Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 374-393, September.
    2. 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.
    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.
    4. 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.
    5. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
    6. 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.
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