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Nonlinear regression modeling via regularized radial basis function networks
Authors:Tomohiro Ando  Sadanori Konishi  Seiya Imoto
Institution:1. Graduate School of Business Administration, Keio University, 2-1-1 Hiyoshi-Honcho, Kohoku-ku, Yokohama 223-8523, Japan;2. Faculty of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan;3. Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo 108-8639, Japan
Abstract:The problem of constructing nonlinear regression models is investigated to analyze data with complex structure. We introduce radial basis functions with hyperparameter that adjusts the amount of overlapping basis functions and adopts the information of the input and response variables. By using the radial basis functions, we construct nonlinear regression models with help of the technique of regularization. Crucial issues in the model building process are the choices of a hyperparameter, the number of basis functions and a smoothing parameter. We present information-theoretic criteria for evaluating statistical models under model misspecification both for distributional and structural assumptions. We use real data examples and Monte Carlo simulations to investigate the properties of the proposed nonlinear regression modeling techniques. The simulation results show that our nonlinear modeling performs well in various situations, and clear improvements are obtained for the use of the hyperparameter in the basis functions.
Keywords:primary 62J02  secondary 62B10
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