Input Variable Selection in Neural Network Models

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 Romano , J. P. , Wolf , M. ( 2005 ). Exact and approximate stepdown methods for multiple hypothesis testing . J. Amer. Statist. Assoc. 100 : 94 – 108 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). 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.