Scoring systems, default probabilities, and certain neural networks

An approach to scoring systems is presented that allows to interpret the output of a simple neural network as a default probability under weak assumptions on the underlying distributions. A learning algorithm is used for a generalized version of the perceptron. This admits as acceptable prior probability distributions (for the output to be interpreted as probability) the general exponential family. As an example the case of two Gaussian priors with different covariance matrices is treated. In addition some preliminary experimental evidence is offered to show the practicability of this approach.