论文标题
使用沙普利值和Mahalanobis距离的多元离群值解释
Multivariate outlier explanations using Shapley values and Mahalanobis distances
论文作者
论文摘要
为了解释多元偏远，可以证明观察的平方Mahalanobis距离可以分解为源自单个变量的偏远贡献。分解是使用Shapley Value获得的，Shapley Value是一种众所周知的游戏理论概念，在可解释的AI的背景下变得很流行。除了异常解释外，该概念还与细胞外倾角的最新表述有关，在该公元中，可以利用shapley值来获得可变贡献，以在鉴于多元数据结构的情况下对其“预期”位置进行外出观察。结合平方的Mahalanobis距离，可以以低的数值成本计算出Shapley值，从而使它们更具吸引力对于离群解释。仿真和现实世界数据示例证明了这些概念的有用性。
For the purpose of explaining multivariate outlyingness, it is shown that the squared Mahalanobis distance of an observation can be decomposed into outlyingness contributions originating from single variables. The decomposition is obtained using the Shapley value, a well-known concept from game theory that became popular in the context of Explainable AI. In addition to outlier explanation, this concept also relates to the recent formulation of cellwise outlyingness, where Shapley values can be employed to obtain variable contributions for outlying observations with respect to their "expected" position given the multivariate data structure. In combination with squared Mahalanobis distances, Shapley values can be calculated at a low numerical cost, making them even more attractive for outlier interpretation. Simulations and real-world data examples demonstrate the usefulness of these concepts.
