Nonlinear regression modeling via the lasso-type regularization |
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Authors: | Shohei Tateishi Hidetoshi Matsui Sadanori Konishi |
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Institution: | 1. Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan;2. Nikon Systems Inc., Queen''s Tower B16F, 2-3-3 Minato-mirai, Nishi-ku, Yokohama 220-6116, Japan;3. Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan |
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Abstract: | We consider the problem of constructing nonlinear regression models with Gaussian basis functions, using lasso regularization. Regularization with a lasso penalty is an advantageous in that it estimates some coefficients in linear regression models to be exactly zero. We propose imposing a weighted lasso penalty on a nonlinear regression model and thereby selecting the number of basis functions effectively. In order to select tuning parameters in the regularization method, we use a deviance information criterion proposed by Spiegelhalter et al. (2002), calculating the effective number of parameters by Gibbs sampling. Simulation results demonstrate that our methodology performs well in various situations. |
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Keywords: | Basis expansion Bayes approach Information criterion Lasso Nonlinear regression Regularization |
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