Input Variable Selection in Neural Network Models

Abstract

One of the most important issues in using neural networks for the analysis of real-world problems is the input variable selection problem. This article connects input variable selection with multiple testing in the neural network regression models. In the proposed procedure, the number and the type of input neurons are selected by means of a testing scheme, based on appropriate measures of relevance of a given input variable to the model. In order to avoid the data snooping problem, family-wise error rate is controlled by using the StepM method proposed by Romano and Wolf (2005). The testing procedure is calibrated by using the subsampling, which is shown to deliver consistent results under weak assumptions on the data generating process and on the structure of the neural network model.

Keywords:

• Multiple testing
• Neural networks
• Subsampling
• Variable selection

Mathematics Subject Classification:

• 62G08, 62H15
• Secondary 62F40, 92B20

Acknowledgments

The authors gratefully acknowledge the helpful comments of two anonymous referees which greatly improved the final version of this article.