  While machine learning (ML) models are increasingly used due to their high
predictive power, their use in understanding the data-generating process (DGP)
is limited. Understanding the DGP requires insights into feature-target
associations, which many ML models cannot directly provide, due to their opaque
internal mechanisms. Feature importance (FI) methods provide useful insights
into the DGP under certain conditions. Since the results of different FI
methods have different interpretations, selecting the correct FI method for a
concrete use case is crucial and still requires expert knowledge. This paper
serves as a comprehensive guide to help understand the different
interpretations of FI methods. Through an extensive review of FI methods and
providing new proofs regarding their interpretation, we facilitate a thorough
understanding of these methods and formulate concrete recommendations for
scientific inference. We conclude by discussing options for FI uncertainty
estimation and point to directions for future research aiming at full
statistical inference from black-box ML models.
