Efficient Distribution-Free Learning of Probabilistic Concepts

In this paper we investigate a new formal model of machine learning in which the concept (boolean function) to be learned may exhibit uncertain or probabilistic behavior|thus, the same input may sometimes be classiied as a positive example and sometimes as a negative example. Such probabilistic concepts (or p-concepts) may arise in situations such as weather prediction, where the measured variables and their accuracy are insuucient to determine the outcome with certainty. We adopt from the Valiant model of learning 27] the demands that learning algorithms be eecient and general in the sense that they perform well for a wide class of p-concepts and for any distribution over the domain. In addition to giving many eecient algorithms for learning natural classes of p-concepts, we study and develop in detail an underlying theory of learning p-concepts.