Significance Tests for Neural Networks

29 Pages Posted: 7 Mar 2019 Last revised: 4 Nov 2020

See all articles by Enguerrand Horel

Enguerrand Horel

Stanford University - Institute for Computational and Mathematical Engineering

Kay Giesecke

Stanford University - Department of Management Science & Engineering

Date Written: November 11, 2018

Abstract

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.

Suggested Citation

Horel, Enguerrand and Giesecke, Kay, Significance Tests for Neural Networks (November 11, 2018). Available at SSRN: https://ssrn.com/abstract=3335592 or http://dx.doi.org/10.2139/ssrn.3335592

Enguerrand Horel (Contact Author)

Stanford University - Institute for Computational and Mathematical Engineering ( email )

Huang Building, 475 Via Ortega
Suite 060 (Bottom level)
Stanford, CA 94305-4042
United States

Kay Giesecke

Stanford University - Department of Management Science & Engineering ( email )

475 Via Ortega
Stanford, CA 94305
United States
(650) 723 9265 (Phone)
(650) 723 1614 (Fax)

HOME PAGE: http://https://giesecke.people.stanford.edu

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