# Strategyproof Linear Regression in High Dimensions

arXiv: https://arxiv.org/abs/1805.10693 · HTML: https://mlsanity.com/paper/1805.10693/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2018.

## Built on by (most cited first, 22 of 22)

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- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
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- [An Equivalence Between Data Poisoning and Byzantine Gradient Attacks](https://mlsanity.com/paper/2202.08578/) (2022)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [Strategic Classification With Externalities](https://mlsanity.com/paper/2410.08032/) (2024)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
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- [Automated Mechanism Design for Classification with Partial Verification](https://mlsanity.com/paper/2104.05182/) (2021)
- [Metric-Fair Classifier Derandomization](https://mlsanity.com/paper/2206.07826/) (2022)
- [To Give or Not to Give? The Impacts of Strategically Withheld Recourse](https://mlsanity.com/paper/2504.05891/) (2025)
- [On the Computational Complexity of Performative Prediction](https://mlsanity.com/paper/2601.20180/) (2026)
- [Strategyproof Learning: Building Trustworthy User-Generated Datasets](https://mlsanity.com/paper/2106.02398/) (2021)
- [Truthful Generalized Linear Models](https://mlsanity.com/paper/2209.07815/) (2022)
- [Fair Clustering: Critique, Caveats, and Future Directions](https://mlsanity.com/paper/2406.15960/) (2024)
- [Strategic Hypothesis Testing](https://mlsanity.com/paper/2508.03289/) (2025)
- [Differentially Private Auditing Under Strategic Response](https://mlsanity.com/paper/2605.07674/) (2026)
- [Strategic Evaluation: Subjects, Evaluators, and Society](https://mlsanity.com/paper/2310.03655/) (2023)

## Abstract (arXiv)

This paper is part of an emerging line of work at the intersection of machine learning and mechanism design, which aims to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms -- and, in fact, their very existence -- are established through a connection to a discrete version of the Ham Sandwich Theorem.