Hypothesis Testing and Machine Learning: Interpreting Variable Effects in Deep Artificial Neural Networks using Cohen's f2

Abstract

Deep artificial neural networks show high predictive performance in many fields, but they do not afford statistical inferences and their black-box operations are too complicated for humans to comprehend. Because positing that a relationship exists is often more important than prediction in scientific experiments and research models, machine learning is far less frequently used than inferential statistics. Additionally, statistics calls for improving the test of theory by showing the magnitude of the phenomena being studied. This article extends current XAI methods and develops a model agnostic hypothesis testing framework for machine learning. First, Fisher's variable permutation algorithm is tweaked to compute an effect size measure equivalent to Cohen's f2 for OLS regression models. Second, the Mann-Kendall test of monotonicity and the Theil-Sen estimator is applied to Apley's accumulated local effect plots to specify a variable's direction of influence and statistical significance. The usefulness of this approach is demonstrated on an artificial data set and a social survey with a Python sandbox implementation.