  Feature attribution is often loosely presented as the process of selecting a
subset of relevant features as a rationale of a prediction. Task-dependent by
nature, precise definitions of "relevance" encountered in the literature are
however not always consistent. 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.
