  The recent increase in the deployment of machine learning models in critical
domains such as healthcare, criminal justice, and finance has highlighted the
need for trustworthy methods that can explain these models to stakeholders.
Feature importance methods (e.g. gain and SHAP) are among the most popular
explainability methods used to address this need. For any explainability
technique to be trustworthy and meaningful, it has to provide an explanation
that is accurate and stable. Although the stability of local feature importance
methods (explaining individual predictions) has been studied before, there is
yet a knowledge gap about the stability of global features importance methods
(explanations for the whole model). Additionally, there is no study that
evaluates and compares the accuracy of global feature importance methods with
respect to feature ordering. In this paper, we evaluate the accuracy and
stability of global feature importance methods through comprehensive
experiments done on simulations as well as four real-world datasets. We focus
on tree-based ensemble methods as they are used widely in industry and measure
the accuracy and stability of explanations under two scenarios: 1) when inputs
are perturbed 2) when models are perturbed. Our findings provide a comparison
of these methods under a variety of settings and shed light on the limitations
of global feature importance methods by indicating their lack of accuracy with
and without noisy inputs, as well as their lack of stability with respect to:
1) increase in input dimension or noise in the data; 2) perturbations in models
initialized by different random seeds or hyperparameter settings.
