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Biometrika 2004 91(1):27-43; doi:10.1093/biomet/91.1.27
© 2004 by Biometrika Trust
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Bayesian information criteria and smoothing parameter selection in radial basis function networks

Sadanori Konishi1, Tomohiro Ando1 and Seiya Imoto2

1 Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan konishi{at}math.kyushu-u.ac.jp ando{at}math.kyushu-u.ac.jp 2 Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo 108-8639, Japan imoto{at}ims.u-tokyo.ac.jp

By extending Schwarz's (1978) basic idea we derive a Bayesian information criterion which enables us to evaluate models estimated by the maximum penalised likelihood method or the method of regularisation.The proposed criterion is applied to the choice of smoothing parameters and the number of basis functions in radial basis function network models. Monte Carlo experiments were conducted to examine the performance of the nonlinear modelling strategy of estimating the weight parameters by regularisation and then determining the adjusted parameters by the Bayesian information criterion. The simulation results show that our modelling procedure performs well in various situations.

Key Words: Bayes approach; Maximum penalised likelihood; Model selection; Neural network; Nonlinear regression

Received December 2001. Revised April 2003


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