Narrowing the Number of Training Cases in Genetic Programming

In Machine Learning, one of the most common and discussed questions is how to choose an adequate number of data that will train the model in a satisfying way, in other words a model that is neither underfitted or overfitted but instead obtains a good generalization ability. The problem grows in importance when we consider Genetic Programming. Indeed, the fitness evaluation is a crucial point regarding the time consumption aspect of this approach, and therefore finding the minimum number of data that allows to discover the underlying structure of the problem could bring considerable benefits. In this thesis we use a concept borrowed from Statistics and Information Theory, the entropy of the target function in symbolic regression problems, in order to develop a possible problem independent solution. We present some examples, numerical and not, in order to show how our theoretical results are confirmed by the simulations.