Significance Tests for Neural Networks
This provides a statistical tool for researchers and practitioners to interpret neural network predictions by identifying influential variables, though it's incremental to existing statistical testing frameworks.
The authors developed a statistical significance test for feature variables in single-layer neural network regression models, proposing a gradient-based test statistic with asymptotic chi-square mixture distribution that enables variable impact assessment and ranking.
We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using nonparametric techniques. Under technical conditions, the limiting distribution is given by a mixture of chi-square distributions. The tests enable one to discern the impact of individual variables on the prediction of a neural network. The test statistic can be used to rank variables according to their influence. Simulation results illustrate the computational efficiency and the performance of the test. An empirical application to house price valuation highlights the behavior of the test using actual data.