Multilayer perceptrons provide an easy to use and flexible technique for non-linear regression. They are defined by their topology, in terms of layers of neurons, and the values of weights and thresholds. A potential difficulty may result from their black box nature and corresponding lack of interpretability, especially if the number of input parameters is large. For this reason, as well as for computational efficiency, we deem it appropriate to preselect a reduced number of input attributes for the multilayer perceptron by first building a regression tree for the considered contingency. On the other hand, multilayer perceptrons show potential in reducing the approximation error of regression trees, due to their continuous modelling capabilities.
Due to space limitations, we refer the interested reader to [12][11] for further information on this by now popular technique. We merely mention that in our experiments we have used single hidden layer perceptrons with sigmoidal activation functions and a batch quasi-Newton ``Broyden-Fletcher-Goldfarb-Shanno'' (BFGS) iterative optimization algorithm to minimize the MSE of eqn. (4).