1 Model Selection for Neural Network Models: A Statistical Perspective
La Rocca Michele, Cira Perna · 2015
It is generally accepted that liner analysis often gives poor performances in approximating real data. Therefore, although it is easy to handle and fast to compute, and many statistical results are available, it cannot be extensively used especially when complex relationships are recognized in the data. In these contexts, it is common the use of non linear analysis which can successfully be employed to reveal these patterns. However, parametric analysis, both linear and nonlinear, requires an “a priori” specification of the links among the variables of interest, which is not always possible. Therefore, even if the results have the advantage of the interpretability (in the sense that the model parameters are often associated to quantities with a “physical” meaning), misspecification problem can arise and can affect seriously the results of the analysis. In this respect, nonparametric analysis seems to be a more effective statistical tool due to its ability to model non-linear phenomena with few (if any) “a priori” assumptions about the nature of the data generating process. Well-studied and frequently used tools in nonparametric analysis include nearest neighbours regression, kernel smoothers, projection pursuit, alternating conditional expectations, average derivative estimation, and classification and regression trees. In this context, computational network analysis forms a field of research which has enjoyed rapid expansion and increasing popularity in both the academic and the research communities, providing an approach that can potentially lead to better non-parametric estimators and providing an interesting framework for unifying different non-parametric paradigms, such as nearest neighbours, kernel smoothers, and projection pursuit. Computational network tools have the advantage, with respect to other nonparametric techniques, to be very flexible tools able to provide, under very general conditions, an arbitrarily accurate approximation to an unknown target the function of interest. Moreover, they are expected to perform better than other non-parametric methods since the approximation form is not so sensitive to the