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Multilayer neural networks and Bayes decision theory
1Center for Mathematical Sciences, The University of Aizu, Aizu-Wakamatsu, Fukushima, Japan
Summary
Multilayer neural networks can approximate Bayes a posteriori probability for pattern classification. This study proves three-layer networks with sufficient hidden units can accurately estimate this probability, providing a theoretical foundation for simulations.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Pattern Recognition
Background:
- Multilayer neural networks are widely used in engineering for pattern classification.
- Recent studies indicate feedforward neural networks can estimate Bayes a posteriori probability via simulation.
Purpose of the Study:
- To theoretically investigate the capability of three-layer neural networks in approximating Bayes a posteriori probability for two-category classification.
- To combine Bayes decision theory with approximation theory for neural networks.
Main Methods:
- Theoretical analysis of three-layer neural networks applied to n-dimensional Gaussian classification.
- Proving the approximation capability of networks with at least 2n hidden units.
- Demonstrating the convergence of network function to a posteriori probability with ideal Back-Propagation learning.
Main Results:
- Theoretically proven that three-layer neural networks with at least 2n hidden units can approximate the a posteriori probability with arbitrary accuracy.
- Proven that the input-output function of these networks converges to the a posteriori probability under ideal Back-Propagation learning conditions.
Conclusions:
- These findings establish a theoretical basis for using computer simulations in pattern classification with neural networks.
- The study validates the use of three-layer neural networks for accurate estimation of Bayes a posteriori probability.