为机器学习解释方法Shapley值提供严格数学证明
Mathematically rigorous proofs for Shapley explanations
- 基于杨的公理体系，严格证明Shapley值唯一性
- 揭示对称性公理不可省略，给出反例证明
- 将Shapley值重构为加权线性回归的唯一解
机器学习在当今世界愈发重要，因此理解其决策过程至关重要。一种常用方法是采用吕德伯格与李提出的Shapley值进行解释。本文从数学严谨性出发，对吕德伯格与李的两项核心结论提供完整证明，原论文未给出这些证明。第一项结果基于杨的公理体系，证明了在局部准确性、缺失性、对称性和一致性条件下，Shapley值是唯一的解释方案。吕德伯格与李认为对称性公理可省略，但本文通过反例表明该公理实际不可或缺。第二项结果表明，Shapley值可被表述为加权线性回归问题的唯一解，证明中使用了维度约简技术。
原文摘要 · Abstract (English)
Machine Learning is becoming increasingly more important in today's world. It is therefore very important to provide understanding of the decision-making process of machine-learning models. A popular way to do this is by looking at the Shapley-Values of these models as introduced by Lundberg and Lee. In this thesis, we discuss the two main results by Lundberg and Lee from a mathematically rigorous standpoint and provide full proofs, which are not available from the original material. The first result of this thesis is an axiomatic characterization of the Shapley values in machine learning based on axioms by Young. We show that the Shapley values are the unique explanation to satisfy local accuracy, missingness, symmetry and consistency. Lundberg and Lee claim that the symmetry axiom is redundant for explanations. However, we provide a counterexample that shows the symmetry axiom is in fact essential. The second result shows that we can write the Shapley values as the unique solution to a weighted linear regression problem. This result is proven with the use of dimensionality reduction.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。