  Feature attribution is often loosely presented as the process of selecting a
subset of relevant features as a rationale of a prediction. This lack of
clarity stems from the fact that we usually do not have access to any notion of
ground-truth attribution and from a more general debate on what good
interpretations are. In this paper we propose to formalise feature
selection/attribution based on the concept of relaxed functional dependence. In
particular, we extend our notions to the instance-wise setting and derive
necessary properties for candidate selection solutions, while leaving room for
task-dependence. By computing ground-truth attributions on synthetic datasets,
we evaluate many state-of-the-art attribution methods and show that, even when
optimised, some fail to verify the proposed properties and provide wrong
solutions.
