Pac learning and artificial neural networks

In this article, we discuss the ‘probably approximately correct’ (PAC) learning paradigm as it applies to artificial neural networks. The PAC learning model is a probabilistic framework for the study of learning and generalization. It is useful not only for neural classification problems, but also for learning problems more often associated with mainstream artificial intelligence, such as the inference of Boolean functions. In PAC theory, the notion of successful learning is formally defined using probability theory. Very roughly speaking, if a large enough sample of randomly drawn training examples is

[1]  Paul W. Goldberg,et al.  Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers , 1993, COLT '93.

[2]  Eduardo D. Sontag,et al.  Finiteness results for sigmoidal “neural” networks , 1993, STOC.

[3]  R. Dudley Central Limit Theorems for Empirical Measures , 1978 .

[4]  Martin Anthony,et al.  Computational Learning Theory for Artificial Neural Networks , 1993 .

[5]  Ronald L. Rivest,et al.  Training a 3-node neural network is NP-complete , 1988, COLT '88.

[6]  Wolfgang Maass,et al.  Bounds for the computational power and learning complexity of analog neural nets , 1993, SIAM J. Comput..

[7]  G. C. Shephard,et al.  Convex Polytopes , 1969, The Mathematical Gazette.

[8]  Wolfgang Maass,et al.  Agnostic PAC Learning of Functions on Analog Neural Nets , 1993, Neural Computation.

[9]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, CACM.

[10]  David Haussler,et al.  Learnability and the Vapnik-Chervonenkis dimension , 1989, JACM.

[11]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[12]  Martin Anthony,et al.  Computational learning theory: an introduction , 1992 .

[13]  David Haussler,et al.  What Size Net Gives Valid Generalization? , 1989, Neural Computation.

[14]  Marek Karpinski,et al.  Polynomial bounds for VC dimension of sigmoidal neural networks , 1995, STOC '95.

[15]  Leslie G. Valiant,et al.  A general lower bound on the number of examples needed for learning , 1988, COLT '88.

[16]  Martin Anthony,et al.  On the power of polynomial discriminators and radial basis function networks , 1993, COLT '93.

[17]  Ronald L. Rivest,et al.  Training a 3-node neural network is NP-complete , 1988, COLT '88.

[18]  David Haussler,et al.  Decision Theoretic Generalizations of the PAC Model for Neural Net and Other Learning Applications , 1992, Inf. Comput..

[19]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .