Principled Architecture Selection for Neural Networks: Application to Corporate Bond Rating Prediction

The notion of generalization ability can be defined precisely as the prediction risk, the expected performance of an estimator in predicting new observations. In this paper, we propose the prediction risk as a measure of the generalization ability of multi-layer perceptron networks and use it to select an optimal network architecture from a set of possible architectures. We also propose a heuristic search strategy to explore the space of possible architectures. The prediction risk is estimated from the available data; here we estimate the prediction risk by v-fold cross-validation and by asymptotic approximations of generalized cross-validation or Akaike's final prediction error. We apply the technique to the problem of predicting corporate bond ratings. This problem is very attractive as a case study, since it is characterized by the limited availability of the data and by the lack of a complete a priori model which could be used to impose a structure to the network architecture. 1 Generalization and Prediction Risk The notion of generalization ability can be defined precisely as the prediction risk, the expected performance of an estimator is predicting new observations. Consider a set of observations D = {(Xj, tj); j = 1 ... N} that are assumed to be generated 683