Nonlinear regression modeling via the lasso-type regularization

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MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」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 reduces some unknown parameters in linear regression models toward 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 model selection criteria derived from information-theoretic and Bayesian viewpoints. Simulation results demonstrate that our methodology performs well in various situations.