We describe an analytical framework for the adaptations of neural systems that adapt its internal structure on the basis of subjective probabilities constructed by computation of randomly received input signals. A principled approach is provided with the key property that it defines a probability density model that allows studying the convergence of the adaptation process. In particular, the derived algorithm can be applied for approximation problems such as the estimation of probability densitiesor the recognition of regression functions. These approximation algorithms can be easily extended to higher-dimensional cases. Certain neural network models can be derived from our approach (e.g., topological feature maps and associative networks).