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Scientists and practitioners increasingly rely on machine learning to modeldata and draw conclusions. Compared to statistical modeling approaches, machinelearning makes fewer explicit assumptions about data structures, such aslinearity. However, their model parameters usually cannot be easily related tothe data generating process. To learn about the modeled relationships, partialdependence (PD) plots and permutation feature importance (PFI) are often usedas interpretation methods. However, PD and PFI lack a theory that relates themto the data generating process. We formalize PD and PFI as statisticalestimators of ground truth estimands rooted in the data generating process. Weshow that PD and PFI estimates deviate from this ground truth due tostatistical biases, model variance and Monte Carlo approximation errors. Toaccount for model variance in PD and PFI estimation, we propose the learner-PDand the learner-PFI based on model refits, and propose corrected variance andconfidence interval estimators.

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