发表机构
National University of Singapore; University of Waterloo; Vector Institute（新加坡国立大学; 滑铁卢大学; 向量研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究合作博弈中归因问题，受最小核心启发引入一类非线性公理归因方法，该方法产生的贡献向量是特定最小化问题的唯一最优解，实验表明其在包含AUC指标上比仅放宽效率公理的夏普利值变体更有效。
AI 中文摘要
夏普利值是归因问题中广泛使用的概念，它唯一满足线性、一致性、平等对待和效率公理。通常用包含AUC指标评估玩家排名质量以识别积极参与玩家，但夏普利值在此目的上并非总是可靠，核心问题在于其线性，零空间过大易包含不可忽略的扰动。为解决此局限，探索非线性公理归因方法设计。受夏普利值的流行非线性替代——最小核心启发，引入保留其余必要公理的一类非线性归因方法。每种方法产生一个贡献向量，是一个最小化问题的唯一最优解，旨在尽可能忠实地逼近效用函数。在包含AUC指标方面，实验证明这些方法相对于仅放宽效率公理的夏普利值变体具有潜在有效性。
英文摘要
The Shapley value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the Shapley value is not always reliable for this purpose. The core issue lies in its linearity: the Shapley value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the Shapley value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to Shapley value variants that relax only the efficiency axiom. Our code is available at https://github.com/watml/nonlinear-axiom.
