Maximum-likelihood design of layered neural networks

The design of layered neural networks is posed as a problem of estimating finite mixtures of normal densities in the framework of statistical decision-making. The output units of the network (third layer) correspond to class-conditional mixtures defined as weighted sums of a given set of normal densities which can be viewed as radial basis functions. It is shown that the resulting classification performance strongly depends on the component densities (second layer) shared by the class conditional mixtures. To enable a global optimization of layered neural networks the EM algorithm is modified to compute m.-l. estimates of finite mixtures with shared components.