Nonlinear regression modeling via regularized radial basis function networks

Tomohiro Ando, Sadanori Konishi, Seiya Imoto

研究成果: Article査読

28 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)3616-3633
ページ数18
ジャーナルJournal of Statistical Planning and Inference
138
11
DOI
出版ステータスPublished - 2008 11月 1

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性
  • 応用数学

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