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Regularization Approach to Nonlinear Variable Selection
Year: 2010  
Authors: Lorenzo Rosasco, Matteo Santoro, Sofia Mosci, Silvia Villa, Alessandro Verri  
Editor: Yee Whye Teh and Mike Titterington Volume: 9
Book title: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (AISTATS2010)
Series: JMLR W&CP Pages: 653-660
Address: Chia Laguna Resort, Sardinia, Italy
Month: May
   
Abstract:
In this paper we consider a regularization approach to variable selection when the regression function depends nonlinearly on a few input variables. The proposed method is based on a regularized least square estimator penalizing large values of the partial derivatives. An efficient iterative procedure is proposed to solve the underlying variational problem, and its convergence is proved. The empirical properties of the obtained estimator are tested both for prediction and variable selection. The algorithm compares favorably to more standard ridge regression and L1 regularization schemes.
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