Neural Networks in Economics: Background, Applications and New Developments
Neural Networks – originally inspired from Neuroscience – p rovide powerful models for statistical data analysis. Their most prominent feature is their a b lity to “learn” dependencies based on a finite number of observations. In the context of Neural Ne tworks the term “learning” means that the knowledge acquired from the samples can be gen eralized to as yet unseen observations. In this sense, a Neural Network is often calle d a Learning Machine. As such, Neural Networks might be considered as a metaphor for an agen t who learns dependencies of his environment and thus infers strategies of behavior ba sed on a limited number of observations. In this contribution, however, we want to abstract from the biological origins of Neural Networks and rather present them as a purely mathematical mo del. The paper is organized as follows: In Section 2 we will summar ize the main results of Statistical Learning Theory which provide a basis for understa nding the generalization properties of existing Neural Network learning algorithms. In Section 3 we will introduce basic concepts and techniques of Neural Network Learning. Then, in Section 4, we will give an overview of existing applications of Neural Networks in Economics. R ecently, however, the ideas from Statistical Learning Theory, as introduced in Section 2, ha ve lead the way to the so called Support Vector learning, which will be described in Section 5 for the task of classification. Finally, in Section 6 we leave the review track and present a s tate–of–the–art application of this technique to the problem of learning the preference structu e from a given set of observations. In contrast to cardinal utility theory our approach is based on ordinal utilities and requires as input only objects together with their respective relation (i.e. preference ranking). Throughout the paper, we will support the theoretical arguments by exam ples.