Non-monotonic Explanation Functions

Explaining black-box classification models is a hot topic in AI, it has the overall goal of improving trust in decisions made by such models. Several works have been done and diverse explanation functions have been proposed. The most prominent ones, like Anchor and LIME, return abductive explanations which highlight key factors that cause predictions. Despite their popularity, the two functions may return inaccurate and sometimes incorrect explanations. In this paper, we study abductive explanations and identify the origin of this shortcoming. We start by defining two kinds of explanations: absolute explanations that are generated from the whole feature space, and plausible explanations (like those provided by Anchors and LIME) that are constructed from a proper subset of the feature space. We show that the former are coherent in that two compatible sets of features cannot explain distinct classes while the latter may however be incoherent, leading thus to incorrect explanations. Then, we show that explanations are provided by non-monotonic functions. Indeed, an explanation may no longer be valid if new instances are received. Finally, we provide a novel function that is based on argumentation and that returns plausible explanations. We show that the function is non monotonic and its explanations are coherent.