  We consider a global representation of a regression or classification
function by decomposing it into the sum of main and interaction components of
arbitrary order. We propose a new identification constraint that allows for the
extraction of interventional SHAP values and partial dependence plots, thereby
unifying local and global explanations. With our proposed identification, a
feature's partial dependence plot corresponds to the main effect term plus the
intercept. The interventional SHAP value of feature $k$ is a weighted sum of
the main component and all interaction components that include $k$, with the
weights given by the reciprocal of the component's dimension. This brings a new
perspective to local explanations such as SHAP values which were previously
motivated by game theory only. We show that the decomposition can be used to
reduce direct and indirect bias by removing all components that include a
protected feature. Lastly, we motivate a new measure of feature importance. In
principle, our proposed functional decomposition can be applied to any machine
learning model, but exact calculation is only feasible for low-dimensional
structures or ensembles of those. We provide an algorithm and efficient
implementation for gradient-boosted trees (xgboost) and random planted forest.
Conducted experiments suggest that our method provides meaningful explanations
and reveals interactions of higher orders. The proposed methods are implemented
in an R package, available at \url{https://github.com/PlantedML/glex}.
