  Machine learning (ML) has seen significant growth in both popularity and
importance. The high prediction accuracy of ML models is often achieved through
complex black-box architectures that are difficult to interpret. This
interpretability problem has been hindering the use of ML in fields like
medicine, ecology and insurance, where an understanding of the inner workings
of the model is paramount to ensure user acceptance and fairness. The need for
interpretable ML models has boosted research in the field of interpretable
machine learning (IML). Here we propose a novel approach for the functional
decomposition of black-box predictions, which is considered a core concept of
IML. The idea of our method is to replace the prediction function by a
surrogate model consisting of simpler subfunctions. Similar to additive
regression models, these functions provide insights into the direction and
strength of the main feature contributions and their interactions. Our method
is based on a novel concept termed stacked orthogonality, which ensures that
the main effects capture as much functional behavior as possible and do not
contain information explained by higher-order interactions. Unlike earlier
functional IML approaches, it is neither affected by extrapolation nor by
hidden feature interactions. To compute the subfunctions, we propose an
algorithm based on neural additive modeling and an efficient post-hoc
orthogonalization procedure.
