Nonlinear regression modeling via regularized radial basis function networks

Tomohiro Ando, Sadanori Konishi, Seiya Imoto

Research output: Contribution to journalArticle

25 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3616-3633
Number of pages18
JournalJournal of Statistical Planning and Inference
Volume138
Issue number11
DOIs
Publication statusPublished - 2008 Nov 1

Keywords

  • Model selection criterion
  • Neural networks
  • Nonlinear logistic model
  • Radial basis functions
  • Regularization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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