# Bayesian Regression Markets

arXiv: https://arxiv.org/abs/2310.14992 · HTML: https://mlsanity.com/paper/2310.14992/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [On the marginal likelihood and cross-validation](https://mlsanity.com/paper/1905.08737/) (2019)
- [Data Pricing in Machine Learning Pipelines](https://mlsanity.com/paper/2108.07915/) (2021)
- [Truthful Linear Regression](https://mlsanity.com/paper/1506.03489/) (2015)
- [Collaborative Machine Learning Markets with Data-Replication-Robust Payments](https://mlsanity.com/paper/1911.09052/) (2019)
- [Regression markets and application to energy forecasting](https://mlsanity.com/paper/2110.03633/) (2021)
- [Towards Data Auctions with Externalities](https://mlsanity.com/paper/2003.08345/) (2020)
- [On the Convergence of the Shapley Value in Parametric Bayesian Learning Games](https://mlsanity.com/paper/2205.07428/) (2022)
- [Multi-period Trading Prediction Markets with Connections to Machine Learning](https://mlsanity.com/paper/1403.0648/) (2014)
- [Data Sharing Markets](https://mlsanity.com/paper/2107.08630/) (2021)
- [Replication-Robust Payoff-Allocation for Machine Learning Data Markets](https://mlsanity.com/paper/2006.14583/) (2020)
- [Trading Data for Wind Power Forecasting: A Regression Market with Lasso Regularization](https://mlsanity.com/paper/2110.07432/) (2021)
- [Selling Information in Competitive Environments](https://mlsanity.com/paper/2202.08780/) (2022)
- [Absolute Shapley Value](https://mlsanity.com/paper/2003.10076/) (2020)

## Built on by (most cited first, 3 of 3)

- [Privacy-Aware Data Acquisition under Data Similarity in Regression Markets](https://mlsanity.com/paper/2312.02611/) (2023)
- [Budget-constrained Collaborative Renewable Energy Forecasting Market](https://mlsanity.com/paper/2501.12367/) (2025)
- [Probabilistic Prediction Markets with Intermittent Contributions](https://mlsanity.com/paper/2510.13385/) (2025)

## Abstract (arXiv)

Although machine learning tasks are highly sensitive to the quality of input data, relevant datasets can often be challenging for firms to acquire, especially when held privately by a variety of owners. For instance, if these owners are competitors in a downstream market, they may be reluctant to share information. Focusing on supervised learning for regression tasks, we develop a regression market to provide a monetary incentive for data sharing. Our mechanism adopts a Bayesian framework, allowing us to consider a more general class of regression tasks. We present a thorough exploration of the market properties, and show that similar proposals in literature expose the market agents to sizeable financial risks, which can be mitigated in our setup.