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Lazy lasso for local regression

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  • Diego Vidaurre
  • Concha Bielza
  • Pedro Larrañaga

Abstract

Locally weighted regression is a technique that predicts the response for new data items from their neighbors in the training data set, where closer data items are assigned higher weights in the prediction. However, the original method may suffer from overfitting and fail to select the relevant variables. In this paper we propose combining a regularization approach with locally weighted regression to achieve sparse models. Specifically, the lasso is a shrinkage and selection method for linear regression. We present an algorithm that embeds lasso in an iterative procedure that alternatively computes weights and performs lasso-wise regression. The algorithm is tested on three synthetic scenarios and two real data sets. Results show that the proposed method outperforms linear and local models for several kinds of scenarios. Copyright Springer-Verlag 2012

Suggested Citation

  • Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2012. "Lazy lasso for local regression," Computational Statistics, Springer, vol. 27(3), pages 531-550, September.
    • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:531-550
    DOI: 10.1007/s00180-011-0274-0
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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. J. Barrientos-Marin & F. Ferraty & P. Vieu, 2010. "Locally modelled regression and functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 617-632.
    3. Scott Foster & Arūnas Verbyla & Wayne Pitchford, 2008. "A random model approach for the LASSO," Computational Statistics, Springer, vol. 23(2), pages 217-233, April.
    4. F. Ferraty & P. Hall & P. Vieu, 2010. "Most-predictive design points for functional data predictors," Biometrika, Biometrika Trust, vol. 97(4), pages 807-824.
    5. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    6. Khan, Jafar A. & Van Aelst, Stefan & Zamar, Ruben H., 2007. "Robust Linear Model Selection Based on Least Angle Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1289-1299, December.
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    Cited by:

    1. M. Bárcena & P. Menéndez & M. Palacios & F. Tusell, 2014. "Alleviating the effect of collinearity in geographically weighted regression," Journal of Geographical Systems, Springer, vol. 16(4), pages 441-466, October.
    2. Vidaurre, Diego & Bielza, Concha & Larrañaga, Pedro, 2013. "Sparse regularized local regression," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 122-135.

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