# Rewarding High-Quality Data via Influence Functions

arXiv: https://arxiv.org/abs/1908.11598 · HTML: https://mlsanity.com/paper/1908.11598/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2019.

## Built on by (most cited first, 11 of 11)

- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [Ten Challenging Problems in Federated Foundation Models](https://mlsanity.com/paper/2502.12176/) (2025)
- [Data Pricing in Machine Learning Pipelines](https://mlsanity.com/paper/2108.07915/) (2021)
- [FedCCEA : A Practical Approach of Client Contribution Evaluation for Federated Learning](https://mlsanity.com/paper/2106.02310/) (2021)
- [FL-Market: Trading Private Models in Federated Learning](https://mlsanity.com/paper/2106.04384/) (2021)
- [Is Shapley Value fair? Improving Client Selection for Mavericks in Federated Learning](https://mlsanity.com/paper/2106.10734/) (2021)
- [GMValuator: Similarity-based Data Valuation for Generative Models](https://mlsanity.com/paper/2304.10701/) (2023)
- [On the Volatility of Shapley-Based Contribution Metrics in Federated Learning](https://mlsanity.com/paper/2405.08044/) (2024)
- [Influence-based Attributions can be Manipulated](https://mlsanity.com/paper/2409.05208/) (2024)
- [Hire When You Need to: Gradual Participant Recruitment for Auction-based Federated Learning](https://mlsanity.com/paper/2310.02651/) (2023)
- [History-Aware and Dynamic Client Contribution in Federated Learning](https://mlsanity.com/paper/2403.07151/) (2024)

## Abstract (arXiv)

We consider a crowdsourcing data acquisition scenario, such as federated learning, where a Center collects data points from a set of rational Agents, with the aim of training a model. For linear regression models, we show how a payment structure can be designed to incentivize the agents to provide high-quality data as early as possible, based on a characterization of the influence that data points have on the loss function of the model. Our contributions can be summarized as follows: (a) we prove theoretically that this scheme ensures truthful data reporting as a game-theoretic equilibrium and further demonstrate its robustness against mixtures of truthful and heuristic data reports, (b) we design a procedure according to which the influence computation can be efficiently approximated and processed sequentially in batches over time, (c) we develop a theory that allows correcting the difference between the influence and the overall change in loss and (d) we evaluate our approach on real datasets, confirming our theoretical findings.