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Robust full Bayesian learning for radial basis networks.

C Andrieu1, N de Freitas, A Doucet

  • 1Cambridge University Engineering Department, Cambridge CB2 1PZ, England.

Neural Computation
|September 26, 2001
PubMed
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We introduce a Bayesian model for radial basis networks, treating network complexity and parameters as random. Our novel reversible-jump Markov chain Monte Carlo (MCMC) method optimizes neural networks and overcomes local minima challenges.

Area of Science:

  • Computational Statistics
  • Machine Learning
  • Artificial Intelligence

Background:

  • Radial basis networks (RBNs) are powerful function approximators.
  • Determining optimal RBN architecture and parameters is challenging.
  • Existing methods often struggle with local minima and prior sensitivity.

Purpose of the Study:

  • To develop a fully Bayesian hierarchical model for RBNs.
  • To introduce a robust and efficient computational method for Bayesian inference in RBNs.
  • To enhance neural network optimization by addressing local minima.

Main Methods:

  • A hierarchical full Bayesian model for RBNs.
  • Reversible-jump Markov chain Monte Carlo (MCMC) for Bayesian computation.
  • A novel reversible-jump MCMC simulated annealing algorithm for neural network optimization.

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Main Results:

  • The proposed Bayesian model and MCMC methods yield superior and robust results compared to previous approaches.
  • The novel algorithm effectively optimizes neural networks by maximizing the joint posterior distribution, mitigating local minima.
  • Demonstrated recovery of classical model selection criteria (AIC, BIC, MDL) within the Bayesian framework.

Conclusions:

  • The hierarchical Bayesian approach provides a flexible and powerful framework for RBNs.
  • The developed MCMC methods offer efficient and robust solutions for Bayesian inference and neural network optimization.
  • The study establishes theoretical convergence properties for the proposed algorithms.