Significance Tests for Neural Networks
Kay Giesecke
Founder, Chairman and Chief Scientist, Professor at Stanford University
Enguerrand Horel
Senior Research Scientist, Upstart
This paper develops 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.
This paper is published in the Journal of Machine Learning Research, volume 21 (227), pages 1−29, 2020.
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About the Speaker
Kay Giesecke
Founder, Chairman and Chief Scientist, Professor at Stanford University
Kay Giesecke is the Founder, Chairman and Chief Scientist at Infima. He is also Professor of Management Science & Engineering at Stanford University, the director of the Advanced Financial Technologies Laboratory, and the director of the Mathematical and Computational Finance Program. Kay serves on the Governing Board and Scientific Advisory Board of the Consortium for Data Analytics in Risk. He is a member of the Council of the Bachelier Finance Society.
Kay is a financial technologist interested in solving the challenging modeling, statistical, and computational problems arising in fixed-income and credit markets. Together with his students at Stanford, Kay has pioneered the core elements of the deep learning and computational technologies underpinning Infima’s solutions.
Kay’s research has won several awards, including the JP Morgan AI Faculty Research Award (2019) and the Fama/DFA Prize (2011), and has been funded by the National Science Foundation, JP Morgan, State Street, Morgan Stanley, Swiss Re, American Express, Moody's,and several other organizations.
Kay has advised several financial technology startups and has been a consultant to banks,investment and risk management firms, governmental agencies, and supranational organizations.
Enguerrand Horel
Senior Research Scientist, Upstart
He obtained his PhD in Computational and Mathematical Engineering at Stanford University, where he developed and analyzed rigorous statistical approaches to explaining the behavior of machine learning models, especially deep learning. During his doctoral studies he worked in the AI Research teams at JP Morgan and Apple.
