Neural Networks - Their Use and Abuse for Small Data Sets

Abstract

Neural networks are commonly used for prediction and classification when data sets are large. They have a big advantage over conventional statistical tools in that it is not necessary to assume any mathematical form for the functional relationship between the variables. However, they also have a few associated problems, chief of which are probably the risk of over-parametrization in the absence of P-values, the lack of appropriate diagnostic tools and the difficulties associated with model interpretation. These problems are particularly pertinent in the case of small data sets. This chapter investigates these problems from a statistical perspective in the context of typical market research data.