LEARNING IN SINGLE HIDDEN-LAYER FEEDFORWARD NETWORK MODELS - BACKPROPAGATION IN A SPATIAL INTERACTION MODELING CONTEXT

Learning in neural networks has attracted considerable interest in rec ent years. Our focus is on learning in single hidden-layar feedforward networks which is posed as a search in the network parameter space fo r a network that minimizes an additive error function of statistically independent examples. We review first the class of single hidden-laye r feedforward networks and characterize the learning process in such n etworks from a statistical point of view, Then we describe the backpro pagation procedure, the leading case of gradient descent learning algo rithms for the class of networks considered here, as well as an effici ent heuristic modification. Finally, we analyze the applicability of t hese learning methods to the problem of predicting interregional telec ommunication flows. Particular emphasis is laid on the engineering jud gment, first, in choosing appropriate values for the tunable parameter s, second, on the decision whether to train the network by epoch or by pattern (random approximation), and, third, on the overfitting proble m. In addition, the analysis shows that the neural network model wheth er using either epoch-based or pattern-based stochastic approximation outperforms the classical regression approach to modeling telecommunic ation flows.