Designing Neural Networks from Statistical Models: A New Approach to Data Exploration

We develop, in the context of discriminant analysis, a general approach to the design of neural architectures. It consists in building a neural net ‘around’ a statistical model family; larger networks, made up of such elementary networks, are then constructed. It is shown that, on the one hand, the statistical modeling approach provides a systematic way to obtaining good approximations in the neural network context, while, on the other, neural networks offer a powerful expansion to classical model families. A novel integrated approach emerges, which stresses both flexibility (contribution of neural nets) and interpretability (contribution of statistical modeling). A well known data set on birth weight is analyzed by this new approach. The results are rather promising and open the way to many potential applications.