Data valuation -- quantifying the contribution of individual data sources to
certain predictive behaviors of a model -- is of great importance to enhancing
the transparency of machine learning and designing incentive systems for data
sharing. Existing work has focused on evaluating data sources with the shared
feature or sample space. How to valuate fragmented data sources of which each
only contains partial features and samples remains an open question. We start
by presenting a method to calculate the counterfactual of removing a fragment
from the aggregated data matrix. Based on the counterfactual calculation, we
further propose 2D-Shapley, a theoretical framework for fragmented data
valuation that uniquely satisfies some appealing axioms in the fragmented data
context. 2D-Shapley empowers a range of new use cases, such as selecting useful
data fragments, providing interpretation for sample-wise data values, and
fine-grained data issue diagnosis.

该研究提出一种计算在聚合的数据矩阵中删除片段的对立假设的方法，并进一步提出了二维 Shapley，这是一种理论框架，旨在评估碎片化的数据源，其在碎片化数据上满足某些有吸引力的公理。 2D-Shapley 赋予了一系列新的用例，例如选择有用的数据片段，提供逐个样本的数据值的解释以及精细的数据问题诊断。