  Complex problems may require sophisticated, non-linear learning methods such
as kernel machines or deep neural networks to achieve state of the art
prediction accuracies. However, high prediction accuracies are not the only
objective to consider when solving problems using machine learning. Instead,
particular scientific applications require some explanation of the learned
prediction function. Unfortunately, most methods do not come with out of the
box straight forward interpretation. Even linear prediction functions are not
straight forward to explain if features exhibit complex correlation structure.
  In this paper, we propose the Measure of Feature Importance (MFI). MFI is
general and can be applied to any arbitrary learning machine (including kernel
machines and deep learning). MFI is intrinsically non-linear and can detect
features that by itself are inconspicuous and only impact the prediction
function through their interaction with other features. Lastly, MFI can be used
for both --- model-based feature importance and instance-based feature
importance (i.e, measuring the importance of a feature for a particular data
point).
