Semivalue-based data valuation uses cooperative-game theory intuitions to assign each data point a value reflecting its contribution to a downstream task. Still, those values depend on the practitioner's choice of utility, raising the question: How robust is semivalue-based data valuation to changes in the utility? This issue is critical when the utility is set as a trade-off between several criteria and when practitioners must select among multiple equally valid utilities. We address this by introducing the notion of a dataset's spatial signature: given a semivalue, we embed each data point into a lower-dimensional space in which any utility becomes a linear functional, making the data valuation framework amenable to a simpler geometric picture. Building on this, we propose a practical methodology centered on an explicit robustness metric that informs practitioners whether and by how much their data valuation results will shift as the utility changes. We validate this approach across diverse datasets and semivalues, demonstrating strong agreement with rank-correlation analyses and offering analytical insight into how choosing a semivalue can amplify or diminish robustness.

翻译：基于半值的数据估值借鉴合作博弈论思想，为每个数据点分配反映其对下游任务贡献的价值。然而，这些价值取决于实践者对效用的选择，从而引出一个关键问题：基于半值的数据估值对效用变化的稳健性如何？当效用被设定为多个标准间的权衡取舍，或实践者必须在多个同等有效的效用函数中进行选择时，这一问题尤为重要。为此，我们引入数据集空间签名的概念：给定一个半值，我们将每个数据点嵌入低维空间，使得任意效用在该空间中均表现为线性泛函，从而将数据估值框架转化为更简洁的几何图景。基于此，我们提出一种以显式稳健性度量为核心的实用方法，该度量能够告知实践者其数据估值结果是否会随效用变化而发生偏移以及偏移的程度。我们在多样化数据集和半值上验证了该方法，结果表明其与秩相关分析高度一致，并为选择特定半值如何增强或削弱稳健性提供了分析性见解。