Interpretable Architecture Neural Networks for Function Visualization

Abstract

In many scientific research fields, understanding and visualizing a black-box function in terms of the effects of all the input variables is of great importance. Existing visualization tools do not allow one to visualize the effects of all the input variables simultaneously. Although one can select one or two of the input variables to visualize via a 2D or 3D plot while holding other variables fixed, this presents an oversimplified and incomplete picture of the model. To overcome this shortcoming, we present a new visualization approach using an Interpretable Architecture Neural Network (IANN) to visualize the effects of all the input variables directly and simultaneously. We propose two interpretable structures, each of which can be conveniently represented by a specific IANN, and we discuss a number of possible extensions. We also provide a Python package to implement our proposed method. The supplemental materials are available online.

KEYWORDS:

• Function visualization
• Interpretable machine learning
• Neural network

Supplementary Materials

Supplemental Materials Several topics will be covered here, including the algorithms for the DASH IANN structure, customized LHD sampling techniques, additional numerical examples, and the proof of Theorem 2.1. (IANN-supplementary.pdf)

Python-package for IANN:Python-package “IANN” containing code to perform the IANN method described in the article and the related datasets. (iann-codes.zip, zipped codes for IANN)

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work was funded in part by the Air Force Office of Scientific Research Grant # FA9550-18-1-0381, which we gratefully acknowledge.