On Preferred Abductive Explanations for Decision Trees and Random Forests

Abstract

Abductive explanations take a central place in eXplainable Artificial Intelligence (XAI) by clarifying with few features the way data instances are classified. However, instances may have exponentially many minimum-size abductive explanations, and this source of complexity holds even for ``intelligible'' classifiers, such as decision trees. When the number of such abductive explanations is huge, computing one of them, only, is often not informative enough. Especially, better explanations than the one that is derived may exist. As a way to circumvent this issue, we propose to leverage a model of the explainee, making precise her / his preferences about explanations, and to compute only preferred explanations. In this paper, several models are pointed out and discussed. For each model, we present and evaluate an algorithm for computing preferred majoritary reasons, where majoritary reasons are specific abductive explanations suited to random forests. We show that in practice the preferred majoritary reasons for an instance can be far less numerous than its majoritary reasons.

On the explanatory power of Boolean decision trees

“…Especially, user preferences, when available, can be used to select explanations of improved quality. It has been shown that the exploitation of user preferences may drastically reduce the number of abductive explanations (60). It would be interesting to evaluate the extent to which handling user preferences (of various kinds) impacts the explanatory importance of features when dealing with decision trees.…”

“…Enumerating minimum-size sufficient reasons An approach to synthesizing the set of sufficient reasons consists in focusing on the minimum-size ones. Indeed, though the set of minimum-size sufficient reasons for an instance given a decision tree can also be exponentially large (60), the number of minimum-size sufficient reasons cannot exceed the number of sufficient reasons, and it can be significantly lower in practice.…”

Logic-Based Explainability in Machine Learning

“…Similarly to the deterministic case, a PAXp is a subset-minimal weak AXp. A set X ⊆ F such that (22) holds is also referred to as relevant set. In the next section, we will illustrate how PAXp's are computed in the case of DTs.…”

“…A key observation is that the feature values that make a path consistent are disjoint from the values that make other paths consistent. This observation allows us to compute the models consistent with each path and, as a result, to compute (22). Let R k ∈ R represent some path in the decision tree.…”

“…Although the existing definitions of (formal) explanations offer important theoretical advantages, e.g. duality of explanations, researchers have looked at alternative definitions, with the purpose of improving the efficiency of algorithms for computing explanations, or improving the expressiveness of explanations [22,23].…”