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Radial basis function networks and complexity regularization in function learning.

A Krzyzak1, T Linder

  • 1Department of Computer Science, Concordia University, Montreal, Quebec, Canada.

IEEE Transactions on Neural Networks
|February 7, 2008
PubMed
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This study introduces complexity regularization for radial basis function networks, enabling broader activation functions and fewer constraints. It establishes estimation bounds for nonlinear function learning with improved convergence rates.

Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Applied Mathematics

Background:

  • Radial basis function (RBF) networks are powerful tools for nonlinear function estimation.
  • Existing complexity regularization methods often impose strict constraints on activation functions and network parameters.
  • There is a need for more flexible and generalizable function learning schemes.

Purpose of the Study:

  • To derive estimation bounds for nonlinear function estimation using RBF networks with complexity regularization.
  • To extend the applicability of complexity regularization to broader classes of activation functions.
  • To analyze the impact of network parameters and loss functions on convergence rates.

Main Methods:

  • Application of complexity regularization techniques.

Related Experiment Videos

  • Utilizing random covering numbers and l(1) metric entropy for broader activation function analysis.
  • Employing empirical risk minimization for network training.
  • Derivation of expected risk bounds based on sample size and loss functions.

    • Main Results:

    • Established estimation bounds for nonlinear function learning with RBF networks.
    • Demonstrated the ability to consider functions of bounded variation, relaxing previous constraints.
    • Obtained bounds on expected risk for a wide range of loss functions.
    • Derived convergence rates to the optimal loss.

    Conclusions:

    • The proposed complexity regularization method offers a more flexible framework for RBF network function learning.
    • The approach successfully generalizes to broader activation functions and relaxes parameter constraints.
    • The derived bounds and convergence rates provide theoretical guarantees for the learning process.