Convergence and Objective Functions of Some Fault/Noise-Injection-Based Online Learning Algorithms for RBF Networks

A rule of thumb for obtaining good generalization in systems trained by examples is that one should use the smallest system that will fit the data. Unfortunately, it usually is not obvious what size is best; a system that is too small will not be able to learn the data while one that is just big enough may learn very slowly and be very sensitive to initial conditions and learning parameters. This paper is a survey of neural network pruning algorithms. The approach taken by the methods described here is to train a network that is larger than necessary and then remove the parts that are not needed.

The problem of model selection, or determination of the number of hidden units, can be approached statistically, by generalizing Akaike's information criterion (AIC) to be applicable to unfaithful (i.e., unrealizable) models with general loss criteria including regularization terms. The relation between the training error and the generalization error is studied in terms of the number of the training examples and the complexity of a network which reduces to the number of parameters in the ordinary statistical theory of AIC. This relation leads to a new network information criterion which is useful for selecting the optimal network model based on a given training set.