On Virtually Binary Nature of Probabilistic Neural Networks

A sequential design of multilayer probabilistic neural networks is considered in the framework of statistical decision-making. Parameters and interconnection structure are optimized layer-by-layer by estimating unknown probability distributions on input space in the form of finite distribution mixtures. The components of mixtures correspond to neurons which perform an information preserving transform between consecutive layers. Simultaneously the entropy of the transformed distribution is minimized. It is argued that in multidimensional spaces and particularly at higher levels of multilayer feedforward neural networks, the output variables of probabilistic neurons tend to be binary. It is shown that the information loss caused by the binary approximation of neurons can be suppressed by increasing the approximation accuracy.