Towards Explaining Deep Learning: Significance Tests for Multi-Layer Perceptrons
33 Pages Posted: 3 Apr 2020
Date Written: March 12, 2020
Horel and Giesecke (2019) (HG) propose a gradient-based test statistic for the one-layer sigmoid neural networks and study its asymptotics using nonparametric techniques. However, their results are not adequate for the most useful and attractive architectures of neural networks, e.g., multi-layer perceptrons. This paper extends their results to the fully connected feed-forward neural networks where the activation function is a general bounded, non-polynomial, and infinitely differentiable (smooth). To derive the test statistic and its asymptotic distribution, we provide the consistency of the multi-layer perceptrons via the method of sieves. Like HG the significant test offers several desirable characteristics such as computational efficiency and ranking variables based on their influence, but, unlike HG the significant test can be used for the multi-layer perceptrons. To validate the theoretical results, a Monte Carlo analysis is presented.
Keywords: Neural Networks, Significant Test, Asymptotic Distribution
JEL Classification: C1, C5
Suggested Citation: Suggested Citation