Rethinking Data Value: Asymmetric Data Shapley for Structure-Aware Valuation in Data Markets and Machine Learning Pipelines

Rigorous valuation of individual data sources is critical for fair compensation in data markets, informed data acquisition, and transparent development of ML/AI models. Classical Data Shapley (DS) provides a essential axiomatic framework for data valuation but is constrained by its symmetry axiom that assumes interchangeability of data sources. This assumption fails to capture the directional and temporal dependencies prevalent in modern ML/AI workflows, including the reliance of duplicated or augmented data on original sources and the order-specific contributions in sequential pipelines such as federated learning and multi-stage LLM fine tuning. To address these limitations, we introduce Asymmetric Data Shapley (ADS), a structure-aware data valuation framework for modern ML/AI pipelines. ADS relaxes symmetry by averaging marginal contributions only over permutations consistent with an application-specific ordering of data groups. It preserves efficiency and linearity, maintains within group symmetry and directional precedence across groups, and reduces to DS when the ordering collapses to a single group. We develop two complementary computational procedures for ADS: (i) a Monte Carlo estimator (MC-ADS) with finite-sample accuracy guarantees, and (ii) a k-nearest neighbor surrogate (KNN-ADS) that is exact and efficient for KNN predictors. Across representative settings with directional and temporal dependence, ADS consistently outperforms benchmark methods by distinguishing novel from redundant contributions and respecting the sequential nature of training. These results establish ADS as a principled and practical approach to equitable data valuation in data markets and complex ML/AI pipelines.