Estimating learning curves by PAC-learnability criterion

This paper improves the sample complexity needed for reliable generalization in the PAC (probably approximately correct) learnability in neural networks, from which the learning curves are estimated. By taking the error supreme over the candidates of network realizations which are attained by minimizing the empirical error, we can refine the order of the sample complexity, whereas the previous methods take the supreme over the whole configuration space. Dimension analysis of concept classes, which is more simple to estimate in real systems than the Vapnik-Chervonenkis (VC) dimension, is introduced for calculating generalization error instead of the traditional VC dimension analysis.