# Data Pricing in Machine Learning Pipelines

arXiv: https://arxiv.org/abs/2108.07915 · HTML: https://mlsanity.com/paper/2108.07915/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 128 references that are in the map.
- First posted on arXiv 18 Aug 2021.

## Builds on (most cited first, 30 of 34)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Stealing Machine Learning Models via Prediction APIs](https://mlsanity.com/paper/1609.02943/) (2016)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [ConCare: Personalized Clinical Feature Embedding via Capturing the Healthcare Context](https://mlsanity.com/paper/1911.12216/) (2019)
- [A Survey on Data Pricing: from Economics to Data Science](https://mlsanity.com/paper/2009.04462/) (2020)
- [Model-based Pricing for Machine Learning in a Data Marketplace](https://mlsanity.com/paper/1805.11450/) (2018)
- [FrugalML: How to Use ML Prediction APIs More Accurately and Cheaply](https://mlsanity.com/paper/2006.07512/) (2020)
- [Crowdsourced Judgement Elicitation with Endogenous Proficiency](https://mlsanity.com/paper/1303.0799/) (2013)
- [Informed Truthfulness in Multi-Task Peer Prediction](https://mlsanity.com/paper/1603.03151/) (2016)
- [Trading Data For Learning: Incentive Mechanism For On-Device Federated Learning](https://mlsanity.com/paper/2009.05604/) (2020)
- [Collaborative Machine Learning Markets with Data-Replication-Robust Payments](https://mlsanity.com/paper/1911.09052/) (2019)
- [Data Collection and Wireless Communication in Internet of Things (IoT) Using Economic Analysis and Pricing Models: A Survey](https://mlsanity.com/paper/1608.03475/) (2016)
- [Double or Nothing: Multiplicative Incentive Mechanisms for Crowdsourcing](https://mlsanity.com/paper/1408.1387/) (2014)
- [Rewarding High-Quality Data via Influence Functions](https://mlsanity.com/paper/1908.11598/) (2019)
- [Revenue Maximization for Query Pricing](https://mlsanity.com/paper/1909.00845/) (2019)
- [Inference Aided Reinforcement Learning for Incentive Mechanism Design in Crowdsourcing](https://mlsanity.com/paper/1806.00206/) (2018)
- [Data Market Platforms: Trading Data Assets to Solve Data Problems](https://mlsanity.com/paper/2002.01047/) (2020)
- [Sequential Peer Prediction: Learning to Elicit Effort using Posted Prices](https://mlsanity.com/paper/1611.09219/) (2016)
- [Deep Bayesian Trust : A Dominant and Fair Incentive Mechanism for Crowd](https://mlsanity.com/paper/1804.05560/) (2018)
- [Approval Voting and Incentives in Crowdsourcing](https://mlsanity.com/paper/1502.05696/) (2015)

## Built on by (most cited first, 18 of 18)

- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Fundamentals of Task-Agnostic Data Valuation](https://mlsanity.com/paper/2208.12354/) (2022)
- [Is Your LLM Overcharging You? Tokenization, Transparency, and Incentives](https://mlsanity.com/paper/2505.21627/) (2025)
- [Data Acquisition: A New Frontier in Data-centric AI](https://mlsanity.com/paper/2311.13712/) (2023)
- [Pricing and Competition for Generative AI](https://mlsanity.com/paper/2411.02661/) (2024)
- [ALinFiK: Learning to Approximate Linearized Future Influence Kernel for Scalable Third-Party LLM Data Valuation](https://mlsanity.com/paper/2503.01052/) (2025)
- [A Survey on Contribution Evaluation in Vertical Federated Learning](https://mlsanity.com/paper/2405.02364/) (2024)
- [Bayesian Regression Markets](https://mlsanity.com/paper/2310.14992/) (2023)
- [Disentangled Structural and Featural Representation for Task-Agnostic Graph Valuation](https://mlsanity.com/paper/2408.12659/) (2024)
- [Compliance Rating Scheme: A Data Provenance Framework for Generative AI Datasets](https://mlsanity.com/paper/2512.21775/) (2025)
- [Data valuation: The partial ordinal Shapley value for machine learning](https://mlsanity.com/paper/2305.01660/) (2023)
- [A Bargaining-based Approach for Feature Trading in Vertical Federated Learning](https://mlsanity.com/paper/2402.15247/) (2024)
- [Online Prompt Pricing based on Combinatorial Multi-Armed Bandit and Hierarchical Stackelberg Game](https://mlsanity.com/paper/2405.15154/) (2024)
- [Distributed In-Context Learning under Non-IID Among Clients](https://mlsanity.com/paper/2408.00144/) (2024)
- [TripleWin: Fixed-Point Equilibrium Pricing for Data-Model Coupled Markets](https://mlsanity.com/paper/2511.03368/) (2025)
- [Trading Vector Data in Vector Databases](https://mlsanity.com/paper/2511.07139/) (2025)
- [Mechanism Design for Federated Learning with Non-Monotonic Network Effects](https://mlsanity.com/paper/2601.04648/) (2026)
- [CHRONOS: Temporally-Aware Multi-Agent Coordination for Evolving Data Marketplaces](https://mlsanity.com/paper/2605.23887/) (2026)

## Abstract (arXiv)

Machine learning is disruptive. At the same time, machine learning can only succeed by collaboration among many parties in multiple steps naturally as pipelines in an eco-system, such as collecting data for possible machine learning applications, collaboratively training models by multiple parties and delivering machine learning services to end users. Data is critical and penetrating in the whole machine learning pipelines. As machine learning pipelines involve many parties and, in order to be successful, have to form a constructive and dynamic eco-system, marketplaces and data pricing are fundamental in connecting and facilitating those many parties. In this article, we survey the principles and the latest research development of data pricing in machine learning pipelines. We start with a brief review of data marketplaces and pricing desiderata. Then, we focus on pricing in three important steps in machine learning pipelines. To understand pricing in the step of training data collection, we review pricing raw data sets and data labels. We also investigate pricing in the step of collaborative training of machine learning models, and overview pricing machine learning models for end users in the step of machine learning deployment. We also discuss a series of possible future directions.