# Model-based Pricing for Machine Learning in a Data Marketplace

arXiv: https://arxiv.org/abs/1805.11450 · HTML: https://mlsanity.com/paper/1805.11450/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2018.

## Built on by (most cited first, 30 of 37)

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- [Data Acquisition: A New Frontier in Data-centric AI](https://mlsanity.com/paper/2311.13712/) (2023)
- [Delegating Data Collection in Decentralized Machine Learning](https://mlsanity.com/paper/2309.01837/) (2023)
- [Pricing and Competition for Generative AI](https://mlsanity.com/paper/2411.02661/) (2024)
- [Fairshare Data Pricing via Data Valuation for Large Language Models](https://mlsanity.com/paper/2502.00198/) (2025)
- [HAPI: A Large-scale Longitudinal Dataset of Commercial ML API Predictions](https://mlsanity.com/paper/2209.08443/) (2022)
- [A Survey of Data Pricing for Data Marketplaces](https://mlsanity.com/paper/2303.04810/) (2023)
- [Proof-of-Contribution-Based Design for Collaborative Machine Learning on Blockchain](https://mlsanity.com/paper/2302.14031/) (2023)
- [Addressing Budget Allocation and Revenue Allocation in Data Market Environments Using an Adaptive Sampling Algorithm](https://mlsanity.com/paper/2306.02543/) (2023)
- [Towards Open Federated Learning Platforms: Survey and Vision from Technical and Legal Perspectives](https://mlsanity.com/paper/2307.02140/) (2023)
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- [Learning Classifiers That Induce Markets](https://mlsanity.com/paper/2502.20012/) (2025)
- [A Sustainable AI Economy Needs Data Deals That Work for Generators](https://mlsanity.com/paper/2601.09966/) (2026)
- [Towards Fair, Robust and Efficient Client Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2402.04409/) (2024)
- [Uncertainty Quantification of Data Shapley via Statistical Inference](https://mlsanity.com/paper/2407.19373/) (2024)
- [Disentangled Structural and Featural Representation for Task-Agnostic Graph Valuation](https://mlsanity.com/paper/2408.12659/) (2024)
- [A Comprehensive Study of Shapley Value in Data Analytics](https://mlsanity.com/paper/2412.01460/) (2024)
- [Data valuation: The partial ordinal Shapley value for machine learning](https://mlsanity.com/paper/2305.01660/) (2023)
- [LossVal: Efficient Data Valuation for Neural Networks](https://mlsanity.com/paper/2412.04158/) (2024)
- [PrivaDE: Privacy-preserving Data Evaluation for Blockchain-based Data Marketplaces](https://mlsanity.com/paper/2510.18109/) (2025)
- [Local Shapley: Model-Induced Locality and Optimal Reuse in Data Valuation](https://mlsanity.com/paper/2603.03672/) (2026)
- [Optimal Pricing for Data-Augmented AutoML Marketplaces](https://mlsanity.com/paper/2310.17843/) (2023)
- [Data Trading Combination Auction Mechanism based on the Exponential Mechanism](https://mlsanity.com/paper/2405.07336/) (2024)

## Abstract (arXiv)

Data analytics using machine learning (ML) has become ubiquitous in science, business intelligence, journalism and many other domains. While a lot of work focuses on reducing the training cost, inference runtime and storage cost of ML models, little work studies how to reduce the cost of data acquisition, which potentially leads to a loss of sellers' revenue and buyers' affordability and efficiency. In this paper, we propose a model-based pricing (MBP) framework, which instead of pricing the data, directly prices ML model instances. We first formally describe the desired properties of the MBP framework, with a focus on avoiding arbitrage. Next, we show a concrete realization of the MBP framework via a noise injection approach, which provably satisfies the desired formal properties. Based on the proposed framework, we then provide algorithmic solutions on how the seller can assign prices to models under different market scenarios (such as to maximize revenue). Finally, we conduct extensive experiments, which validate that the MBP framework can provide high revenue to the seller, high affordability to the buyer, and also operate on low runtime cost.