TABLE OF CONTENTS In the previous section the model structure was assumed to be fixed, and the problem at hand was to estimate the model parameters. Here, the goal is to determine the best model structure, using only the experimental data. Each structure has a different complexity that here denotes the number of parameters to be estimated.
The aim here is to find parsimonious models that have a satisfactory performance for the given data, with the smallest possible complexity. It is known that, as the model complexity increases, for the same amount of training data, the model performance in this data set improves but, above a certain limit in the complexity, the model performance in the test data is deteriorated. There is a compromise between the approximation obtained in the training set and the generalisation in data not seen by the model. The final goal of any structure selection method is to find this compromise value. If the model complexity is below it, we are in the presence of underfitting or undermodelling; if, on the other hand the model complexity is above that value, there is overfitting or overmodelling. The determination of this compromise value is a difficult problem as, besides assuming that one of the methods described in the last section is able to find the optimal model (with the additional problem of the existence of local minima), this compromise value in practice depends on the amount and on the quality of the training data.
Before specifying methods for...
