arXiv:2501.06078cs.LGcs.AI2025-01被引 14

为近邻分类提供基于特征的可解释性分析,揭示关键特征如何影响分类结果。

Explaining k-Nearest Neighbors: Abductive and Counterfactual Explanations

  • 从特征角度出发,研究最小充分理由与最小距离反事实解释
  • 证明在高维空间中特征重要性难以判断,需依赖优化方法求解
  • 利用整数二次规划与SAT求解器实现实际可解释性计算

尽管k-最近邻分类器被广泛应用,但其可解释性在理论上仍不清晰。传统从数据角度的解释(即指出决定输入向量分类的k个训练样本)在高维场景下不实用,因特征数量多且重要性不明。本文转向特征视角,研究两类解释:一是最小充分理由(abductive explanations),即足以保证分类结果的特征子集;二是基于最小距离特征变动的反事实解释(counterfactual explanations)。我们系统分析了离散与连续特征空间下,不同距离函数对解释复杂度的影响,得出正负复杂性结论。最后表明,尽管存在理论困难,通过整数二次规划与SAT求解仍可在实践中计算出有效解释。

原文摘要 · Abstract (English)

Despite the wide use of $k$-Nearest Neighbors as classification models, their explainability properties remain poorly understood from a theoretical perspective. While nearest neighbors classifiers offer interpretability from a ``data perspective'', in which the classification of an input vector $\bar{x}$ is explained by identifying the vectors $\bar{v}_1, \ldots, \bar{v}_k$ in the training set that determine the classification of $\bar{x}$, we argue that such explanations can be impractical in high-dimensional applications, where each vector has hundreds or thousands of features and it is not clear what their relative importance is. Hence, we focus on understanding nearest neighbor classifications through a ``feature perspective'', in which the goal is to identify how the values of the features in $\bar{x}$ affect its classification. Concretely, we study abductive explanations such as ``minimum sufficient reasons'', which correspond to sets of features in $\bar{x}$ that are enough to guarantee its classification, and counterfactual explanations based on the minimum distance feature changes one would have to perform in $\bar{x}$ to change its classification. We present a detailed landscape of positive and negative complexity results for counterfactual and abductive explanations, distinguishing between discrete and continuous feature spaces, and considering the impact of the choice of distance function involved. Finally, we show that despite some negative complexity results, Integer Quadratic Programming and SAT solving allow for computing explanations in practice.

可解释性近邻分类特征重要性反事实

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