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Nonparametric estimation and classification using radial basis function nets and empirical risk minimization.

A Krzyzak1, T Linder, C Lugosi

  • 1Dept. of Comput. Sci., Concordia Univ., Montreal, Que.

IEEE Transactions on Neural Networks
|January 1, 1996
PubMed
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This study analyzes radial basis function (RBF) networks, demonstrating their consistency for nonlinear function approximation and nonparametric classification using empirical risk minimization. The findings are crucial for advancing machine learning algorithms.

Area of Science:

  • Machine Learning
  • Computational Statistics

Background:

  • Radial basis function (RBF) networks are a class of artificial neural networks.
  • Their convergence properties are crucial for understanding their effectiveness in complex tasks.

Purpose of the Study:

  • To investigate the convergence properties of RBF networks for a broad range of basis functions.
  • To review existing methods and results concerning RBF network convergence.
  • To establish the consistency of RBF networks in function approximation and classification.

Main Methods:

  • Empirical risk minimization was used to determine network parameters.
  • Analysis involved distribution-free nonasymptotic probability inequalities.
  • Covering numbers for function classes were employed.

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Main Results:

  • Optimal RBF networks demonstrate consistency in nonlinear function approximation.
  • RBF networks are shown to be consistent in nonparametric classification.
  • Two classification approaches were analyzed: nonlinear function estimation and direct empirical error minimization.

Conclusions:

  • The study confirms the theoretical underpinnings of RBF network performance.
  • Findings support the use of RBF networks in machine learning for approximation and classification.
  • The employed analytical tools provide a robust framework for evaluating learning algorithms.