Abstract
We investigate a net regularization method for variable selection in the linear model, which has convex loss function and concave penalty. Meanwhile, the net regularization based on the use of the Lr penalty with \(\frac{1}{2}\leq\) r ≤1. In the simulation we will demonstrate that the net regularization is more efficient and more accurate for variable selection than Lasso.
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References
Mallows, C.L.: Some comments on Cp. Technometrics 15(4), 661–675 (1973)
Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, F. (eds.) Second International Symposium on Information Theory, pp. 267–281. Akademiai Kiado, Budapest (1973)
Schwarz, G.: Estimating the dimension of a model. Ann. Statist. 6, 461–464 (1978)
Breiman, L.: Heuristics of instability and stabilization in model selection. Ann. Statist. 24, 2350–2383 (1996)
Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. Royal Statist. Soc., B 58, 267–288 (1996)
Donoho, D.L., Huo, X.: Uncertainty principles and ideal atomic decomposition. IEEE Transaction on Information Theory 47, 2845–2862 (2001)
Donoho, D.L., Elad, E.: Maximal sparsity representation via l1 minimization. Proceedings of the National Academy of Sciences 100, 2197–2202 (2003)
Zou, H., Hastie, T.: Regularization and variable seection via the elastic net. Journal of the Royal Statistical Society, Series B 67, 301–320 (2005)
Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96, 1348–1360 (2001)
Zhao, P., Yu, B.: Stagewise Lasso. Journal of Machine Learning Research 8, 2701–2726 (2007)
Knight, K., Fu, W.J.: Asymptotics for lasso-type estimators. Annals of Statistics 28, 1356–1378 (2000)
Friedman, J.H.: Fast Sparse Regression and Classfication. Stanford University, Dept. of Statistics technical report (2008)
Zhang, H., Liang, Y., Wang, Y., Xu, Z.: A net regularization for variable selection via nonconvex penalty (Submitted to Sci. China Ser. F) (2011)
Stamey, T., Kabalin, J., McNeal, J., et al.: Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate ii:radical prostatectomy treated patients. J. Urol. 16, 1076–1083 (1989)
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Luan, XZ. et al. (2012). Regularization Path for Linear Model via Net Method. In: Tan, Y., Shi, Y., Ji, Z. (eds) Advances in Swarm Intelligence. ICSI 2012. Lecture Notes in Computer Science, vol 7332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31020-1_49
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DOI: https://doi.org/10.1007/978-3-642-31020-1_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31019-5
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