Supervised Learning of Probability Distributions by Neural Networks

In the past thirty years many researchers have studied the question of supervised learning in'neural'-like networks. Recently a learning algorithm called'back propagation H - 4 or the'general(cid:173) ized delta-rule' has been applied to numerous problems including the mapping of text to phonemes 5, the diagnosis of illnesses6 and the classification of sonar targets 7 • In these applications, it would often be natural to consider imperfect, or probabilistic informa(cid:173) tion.