Widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models on the one hand and a number of crucial issues pertaining to them warrant the need for explainable artificial intelligence (XAI). A key explainability question is: given this decision was made, what are the input features which contributed to the decision? Although a range of XAI approaches exist to tackle this problem, most of them have significant limitations. Heuristic XAI approaches suffer from the lack of quality guarantees, and often try to approximate Shapley values, which is not the same as explaining which features contribute to a decision. A recent alternative is so-called formal feature attribution (FFA), which defines feature importance as the fraction of formal abductive explanations (AXp's) containing the given feature. This measures feature importance from the view of formally reasoning about the model's behavior. It is challenging to compute FFA using its definition because that involves counting AXp's, although one can approximate it. Based on these results, this paper makes several contributions. First, it gives compelling evidence that computing FFA is intractable, even if the set of contrastive formal explanations (CXp's) is provided, by proving that the problem is #P-hard. Second, by using the duality between AXp's and CXp's, it proposes an efficient heuristic to switch from CXp enumeration to AXp enumeration on-the-fly resulting in an adaptive explanation enumeration algorithm effectively approximating FFA in an anytime fashion. Finally, experimental results obtained on a range of widely used datasets demonstrate the effectiveness of the proposed FFA approximation approach in terms of the error of FFA approximation as well as the number of explanations computed and their diversity given a fixed time limit.

翻译：人工智能（AI）算法和机器学习（ML）模型的广泛使用，以及与之相关的若干关键问题，使得可解释人工智能（XAI）成为必要。一个关键的可解释性问题是：在给定决策结果的前提下，哪些输入特征对该决策产生了贡献？尽管存在一系列XAI方法来解决这一问题，但大多数方法都有显著局限性。启发式XAI方法缺乏质量保证，且通常试图近似沙普利值，这与解释哪些特征对决策有贡献并非同一概念。最近的一种替代方案是所谓的正式特征归因（FFA），它将特征重要性定义为包含该特征的正式溯因解释（AXp）所占的比例。这从形式化推理模型行为的角度衡量特征重要性。由于这涉及对AXp进行计数，因此直接利用其定义计算FFA颇具挑战性，不过可以对其进行近似。基于这些结果，本文做出多项贡献。首先，通过证明该问题为#P-hard，提供了令人信服的证据表明计算FFA是棘手的，即使已提供对比性正式解释（CXp）集合也是如此。其次，利用AXp与CXp之间的对偶性，提出了一种高效启发式方法，可动态地从CXp枚举切换至AXp枚举，从而得到一种自适应的解释枚举算法，能够以随时方式有效近似FFA。最后，在多个广泛使用的数据集上获得的实验结果，从FFA近似的误差、给定时间限制内计算出的解释数量及其多样性等方面，证明了所提出的FFA近似方法的有效性。