Equitable Data Valuation Meets the Right to Be Forgotten in Model Markets

The increasing demand for data-driven machine learning (ML) models has led to the emergence of model markets, where a broker collects personal data from data owners to produce high-usability ML models. To incentivize data owners to share their data, the broker needs to price data appropriately while protecting their privacy. For equitable data valuation, which is crucial in data pricing, Shapley value has become the most prevalent technique because it satisfies all four desirable properties in fairness: balance, symmetry, zero element, and additivity. For the right to be forgotten, which is stipulated by many data privacy protection laws to allow data owners to unlearn their data from trained models, the sharded structure in ML model training has become a de facto standard to reduce the cost of future unlearning by avoiding retraining the entire model from scratch. In this paper, we explore how the sharded structure for the right to be forgotten affects Shapley value for equitable data valuation in model markets. To adapt Shapley value for the sharded structure, we propose S-Shapley value, a sharded structure-based Shapley value, which satisfies four desirable properties for data valuation. Since we prove that computing S-Shapley value is #P-complete, two sampling-based methods are developed to approximate S-Shapley value. Furthermore, to efficiently update valuation results after data owners unlearn their data, we present two delta-based algorithms that estimate the change of data value instead of the data value itself. Experimental results demonstrate the efficiency and effectiveness of the proposed algorithms.