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High-quality machine learning models are dependent on access to high-qualitytraining data. When the data are not already available, it is tedious andcostly to obtain them. Data markets help with identifying valuable trainingdata: model consumers pay to train a model, the market uses that budget toidentify data and train the model (the budget allocation problem), and finallythe market compensates data providers according to their data contribution(revenue allocation problem). For example, a bank could pay the data market toaccess data from other financial institutions to train a fraud detection model.Compensating data contributors requires understanding data's contribution tothe model; recent efforts to solve this revenue allocation problem based on theShapley value are inefficient to lead to practical data markets.  In this paper, we introduce a new algorithm to solve budget allocation andrevenue allocation problems simultaneously in linear time. The new algorithmemploys an adaptive sampling process that selects data from those providers whoare contributing the most to the model. Better data means that the algorithmaccesses those providers more often, and more frequent accesses corresponds tohigher compensation. Furthermore, the algorithm can be deployed in bothcentralized and federated scenarios, boosting its applicability. We providetheoretical guarantees for the algorithm that show the budget is usedefficiently and the properties of revenue allocation are similar to Shapley's.Finally, we conduct an empirical evaluation to show the performance of thealgorithm in practical scenarios and when compared to other baselines. Overall,we believe that the new algorithm paves the way for the implementation ofpractical data markets.

Addressing Budget Allocation and Revenue Allocation in Data Market Environments Using an Adaptive Sampling Algorithm