# Truthful Linear Regression

arXiv: https://arxiv.org/abs/1506.03489 · HTML: https://mlsanity.com/paper/1506.03489/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2015.

## Built on by (most cited first, 13 of 13)

- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [FL-Market: Trading Private Models in Federated Learning](https://mlsanity.com/paper/2106.04384/) (2021)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [SelectMix: Enhancing Label Noise Robustness through Targeted Sample Mixing](https://mlsanity.com/paper/2509.11265/) (2025)
- [Optimal Scoring Rule Design under Partial Knowledge](https://mlsanity.com/paper/2107.07420/) (2021)
- [Differentially Private Synthetic Control](https://mlsanity.com/paper/2303.14084/) (2023)
- [Bayesian Regression Markets](https://mlsanity.com/paper/2310.14992/) (2023)
- [Truthful Generalized Linear Models](https://mlsanity.com/paper/2209.07815/) (2022)
- [Privacy-Aware Data Acquisition under Data Similarity in Regression Markets](https://mlsanity.com/paper/2312.02611/) (2023)
- [How to Purchase Labels? A Cost-Effective Approach Using Active Learning Markets](https://mlsanity.com/paper/2511.20605/) (2025)
- [Information Design Against Gaming and Learning Adversaries](https://mlsanity.com/paper/2609.31643/) (2026)

## Abstract (arXiv)

We consider the problem of fitting a linear model to data held by individuals who are concerned about their privacy. Incentivizing most players to truthfully report their data to the analyst constrains our design to mechanisms that provide a privacy guarantee to the participants; we use differential privacy to model individuals' privacy losses. This immediately poses a problem, as differentially private computation of a linear model necessarily produces a biased estimation, and existing approaches to design mechanisms to elicit data from privacy-sensitive individuals do not generalize well to biased estimators. We overcome this challenge through an appropriate design of the computation and payment scheme.