Relating the Partial Dependence Plot and Permutation Feature Importance to the Data Generating Process

Abstract

AbstractScientists and practitioners increasingly rely on machine learning to model data and draw conclusions. Compared to statistical modeling approaches, machine learning makes fewer explicit assumptions about data structures, such as linearity. Consequently, the parameters of machine learning models usually cannot be easily related to the data generating process. To learn about the modeled relationships, partial dependence (PD) plots and permutation feature importance (PFI) are often used as interpretation methods. However, PD and PFI lack a theory that relates them to the data generating process. We formalize PD and PFI as statistical estimators of ground truth estimands rooted in the data generating process. We show that PD and PFI estimates deviate from this ground truth not only due to statistical biases, but also due to learner variance and Monte Carlo approximation errors. To account for these uncertainties in PD and PFI estimation, we propose the learner-PD and the learner-PFI based on model refits and propose corrected variance and confidence interval estimators.