An estimation of sample complexity of the neural network model in the extended PAC learning framework
S. Miyake, Fumio Kanaya · 2003
L.G. Valiant's (1984) PAC (probably approximately correct) learning framework is extended to be applicable to the statistical decision theoretic problem setting. In this general setting, successful learning means finding a hypothesis or a decision rule that attains risk that is as close as possible to Bayes optimal risk. It is then shown that the generalization ability of a learning model in the extended PAC framework can be consistently considered from the Bayes risk consistency viewpoint. Finally, as an application of the extended PAC framework, an upper bound on the sample complexity of a neural network model is obtained. The upper bound is equal in the order of the PAC learning parameters epsilon and delta to the one that D. Haussler obtained (1989). However, the lower bound on sample complexity and the tightness of these upper bounds are remaining problems.>