  Scientists 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. However, their model parameters 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 due to
statistical biases, model variance and Monte Carlo approximation errors. To
account for model variance 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.
