Bayesowskie sieci neuronowe w analizie problemów regresji

The lecture entitled "Bayesian Neural Networks in the Analysis of Regression Problems" deals with basics of the Bayesian inference (BI) and its various methods and relations to the Standard Neural Networks (SNNs). In subsequent Sections the following problems are discussed: 1) Bayesian Neural Networks (BNNs) as a fusing of SNN and BI; 2) The regression and Feed-forward Layered Neural Network (FLNN); 3) Principles of BI; 4) Maximum Likelihood (ML) and Maximum APosterior (MAP) methods; 5) Criterion of Maximum EVidence (MEV), 6)Types of BNNs. Special attention is focused on the application of MAP for the controlling the over-fitting of the neural approximation. The MEV is also explored for the design of deterministic networks FLNN/MAP. The more extended application of BI enables to formulate a semi-probabilistic simple network S-BNN and a truly probabilistic Bayesian network T-BNN. A numerical efficiency of the Bayesian methods and networks is discussed in paper [1] presented at the XIII Symposium DYNKON2008.