发表机构
Computer science Research Institute of Lens (CRIL), UMR CNRS 8188, University of Artois（朗斯计算机科学研究所（CRIL），CNRS UMR 8188，阿尔图瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于稀疏锚定线性模型的统一概率可解释框架，适用于分类与回归，通过布尔超立方体映射捕捉特征贡献，并证明其相关性误差有界，实验优于LIME和MAPLE。
AI 中文摘要
形式化可解释性为单个预测提供了数学上严谨的依据。然而，溯因解释往往涉及过多特征，超出人类认知极限，而概率松弛方法在很大程度上仍局限于分类任务。我们提出了一个基于稀疏、锚定线性模型的统一概率可解释性框架，适用于二分类和连续回归任务。通过将实例映射到布尔超立方体，我们的线性解释严格推广了基于子集的方法：它们既捕捉特征贡献的幅度和方向，又强制执行预设的稀疏度预算 $k$。我们证明，当底层模型为神经网络时，最小化此类解释的相关性误差是 \ClassNPPP-难的，并将这一难解目标与一个可处理的替代目标——保真度误差——联系起来。对于参数化的局部分布族，任何 $k$-稀疏解释的相关性误差都以其保真度误差为上界，且乘性因子在局部保持较小。我们通过两种互补方法解决由此产生的经验问题：一种混合整数规划（MIP）公式，能在保持多项式样本复杂度的同时产生可证明最优的经验解；以及一种具有可证明近似保证的多项式时间迭代硬阈值（IHT）算法。实证评估表明，与LIME和MAPLE等最先进基线不同，我们的解释在构造上同时满足锚定和稀疏性约束，并持续实现更低的相关性误差。
英文摘要
Formal explainability provides mathematically grounded justifications for individual predictions. However, abductive explanations often exceed human cognitive limits by involving too many features, while probabilistic relaxations have remained largely limited to categorical classification. We present a unified framework for probabilistic explainability based on sparse, anchored linear models, applicable to both binary classification and continuous regression. By mapping instances to the Boolean hypercube, our linear explanations strictly generalize subset-based approaches: they capture both the magnitude and direction of feature contributions while enforcing a prescribed sparsity budget $k$. We show that minimizing the relevance error for such explanations is \ClassNPPP-hard when the underlying model is a neural network, and we relate this intractable objective to a tractable surrogate---the fidelity error. For a parameterized family of local distributions, the relevance error of any $k$-sparse explanation is bounded by its fidelity error up to a multiplicative factor that remains small locally. We address the resulting empirical problem using two complementary approaches: a Mixed Integer Programming (MIP) formulation that yields provably optimal empirical solutions while maintaining polynomial sample complexity, and a polynomial-time Iterative Hard Thresholding (IHT) algorithm with provable approximation guarantees. Empirical evaluations show that, unlike state-of-the-art baselines such as LIME and MAPLE, our explanations satisfy both the anchoring and sparsity constraints by construction, while consistently achieving lower relevance error.
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