Probabilistic Analysis of Learning in Arti cial Neural Networks: The PAC Model and its Variants

There are a number of mathematical approaches to the study of learning and generalization in arti cial neural networks. Here we survey the `probably approximately correct' (PAC) model of learning and some of its variants. These models provide a probabilistic framework for the discussion of generalization and learning. This survey concentrates on the sample complexity questions in these models; that is, the emphasis is on how many examples should be used for training. Computational complexity considerations are brie y discussed for the basic PAC model. Throughout, the importance of the Vapnik-Chervonenkis dimension is highlighted. Particular attention is devoted to describing how the probabilistic models apply in the context of neural network learning, both for networks with binary-valued output and for networks with real-valued output.