Nonlinear regression modeling via regularized radial basis function networks

Tomohiro Ando, Sadanori Konishi, Seiya Imoto

Research output: Contribution to journalArticle

23 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

Fingerprint

Radial basis function networks
Radial Basis Function Network
Nonlinear Regression
Basis Functions
Hyperparameters
Nonlinear Regression Model
Modeling
Radial Functions
Model Misspecification
Nonlinear Modeling
Smoothing Parameter
Complex Structure
Statistical Model
Overlapping
Regularization
Monte Carlo Simulation
Radial basis function
Nonlinear regression
Regression model
Simulation

Keywords

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

ASJC Scopus subject areas

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

Cite this

Nonlinear regression modeling via regularized radial basis function networks. / Ando, Tomohiro; Konishi, Sadanori; Imoto, Seiya.

In: Journal of Statistical Planning and Inference, Vol. 138, No. 11, 01.11.2008, p. 3616-3633.

Research output: Contribution to journalArticle

Ando, Tomohiro ; Konishi, Sadanori ; Imoto, Seiya. / Nonlinear regression modeling via regularized radial basis function networks. In: Journal of Statistical Planning and Inference. 2008 ; Vol. 138, No. 11. pp. 3616-3633.
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