In this paper, we investigate the computational intelligibility of Boolean classifiers, characterized by their ability to answer XAI queries in polynomial time. The classifiers under consideration are decision trees, DNF formulae, decision lists, decision rules, tree ensembles, and Boolean neural nets. Using 9 XAI queries, including both explanation queries and verification queries, we show the existence of large intelligibility gap between the families of classifiers. On the one hand, all the 9 XAI queries are tractable for decision trees. On the other hand, none of them is tractable for DNF formulae, decision lists, random forests, boosted decision trees, Boolean multilayer perceptrons, and binarized neural networks.

Random forests have long been considered as powerful model ensembles in machine learning. By training multiple decision trees, whose diversity is fostered through data and feature subsampling, the resulting random forest can lead to more stable and reliable predictions than a single decision tree. This however comes at the cost of decreased interpretability: while decision trees are often easily interpretable, the predictions made by random forests are much more difficult to understand, as they involve a majority vote over multiple decision trees. In this paper, we examine different types of reasons that explain "why" an input instance is classified as positive or negative by a Boolean random forest. Notably, as an alternative to prime-implicant explanations taking the form of subset-minimal implicants of the random forest, we introduce majoritary reasons which are subset-minimal implicants of a strict majority of decision trees. For these abductive explanations, the tractability of the generation problem (finding one reason) and the optimization problem (finding one minimum-sized reason) are investigated. Unlike prime-implicant explanations, majoritary reasons may contain redundant features. However, in practice, prime-implicant explanations - for which the identification problem is DP-complete - are slightly larger than majoritary reasons that can be generated using a simple linear-time greedy algorithm. They are also significantly larger than minimum-sized majoritary reasons which can be approached using an anytime Partial MaxSAT algorithm.

No 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.

In this paper, we investigate the computational intelligibility of Boolean classifiers, characterized by their ability to answer XAI queries in polynomial time. The classifiers under consideration are decision trees, DNF formulae, decision lists, decision rules, tree ensembles, and Boolean neural nets. Using 9 XAI queries, including both explanation queries and verification queries, we show the existence of large intelligibility gap between the families of classifiers. On the one hand, all the 9 XAI queries are tractable for decision trees. On the other hand, none of them is tractable for DNF formulae, decision lists, random forests, boosted decision trees, Boolean multilayer perceptrons, and binarized neural networks.