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Bayesian information criteria and smoothing parameter selection in radial basis function networks

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  • Sadanori Konishi

Abstract

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. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:1:p:27-43
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    Cited by:

    1. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    2. Ando, Tomohiro & Tsay, Ruey, 2010. "Predictive likelihood for Bayesian model selection and averaging," International Journal of Forecasting, Elsevier, vol. 26(4), pages 744-763, October.
    3. Matsui, Hidetoshi & Konishi, Sadanori, 2011. "Variable selection for functional regression models via the L1 regularization," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3304-3310, December.
    4. Ando, Tomohiro, 2009. "Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1717-1726, September.
    5. Hidetoshi Matsui & Takamitsu Araki & Sadanori Konishi, 2011. "Multiclass Functional Discriminant Analysis and Its Application to Gesture Recognition," Journal of Classification, Springer;The Classification Society, vol. 28(2), pages 227-243, July.
    6. Matsui, Hidetoshi, 2014. "Variable and boundary selection for functional data via multiclass logistic regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 176-185.
    7. M. Rincón & M. Ruiz-Medina, 2012. "Wavelet-RKHS-based functional statistical classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(3), pages 201-217, October.
    8. Ando, Tomohiro, 2009. "Bayesian inference for the hazard term structure with functional predictors using Bayesian predictive information criteria," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1925-1939, April.
    9. Matsui, Hidetoshi, 2020. "Quadratic regression for functional response models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 125-136.
    10. Duchwan Ryu & Devrim Bilgili & Önder Ergönül & Faming Liang & Nader Ebrahimi, 2018. "A Bayesian Generalized Linear Model for Crimean–Congo Hemorrhagic Fever Incidents," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 153-170, March.
    11. Fujii, Toru & Konishi, Sadanori, 2006. "Nonlinear regression modeling via regularized wavelets and smoothing parameter selection," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2023-2033, October.
    12. Tomohiro Ando & Sadanori Konishi, 2009. "Nonlinear logistic discrimination via regularized radial basis functions for classifying high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 331-353, June.
    13. Masao Ueki & Kaoru Fueda, 2010. "Optimal tuning parameter estimation in maximum penalized likelihood method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 413-438, June.

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