# Linear Regression from Strategic Data Sources

arXiv: https://arxiv.org/abs/1309.7824 · HTML: https://mlsanity.com/paper/1309.7824/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2013.

## Built on by (most cited first, 6 of 6)

- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)
- [Learning with Exposure Constraints in Recommendation Systems](https://mlsanity.com/paper/2302.01377/) (2023)
- [Combinatorial Bandits under Strategic Manipulations](https://mlsanity.com/paper/2102.12722/) (2021)
- [Strategic Linear Contextual Bandits](https://mlsanity.com/paper/2406.00551/) (2024)
- [Long-term Data Sharing under Exclusivity Attacks](https://mlsanity.com/paper/2201.09137/) (2022)
- [COBRA: Contextual Bandit Algorithm for Ensuring Truthful Strategic Agents](https://mlsanity.com/paper/2505.23720/) (2025)

## Abstract (arXiv)

Linear regression is a fundamental building block of statistical data analysis. It amounts to estimating the parameters of a linear model that maps input features to corresponding outputs. In the classical setting where the precision of each data point is fixed, the famous Aitken/Gauss-Markov theorem in statistics states that generalized least squares (GLS) is a so-called "Best Linear Unbiased Estimator" (BLUE). In modern data science, however, one often faces strategic data sources, namely, individuals who incur a cost for providing high-precision data. In this paper, we study a setting in which features are public but individuals choose the precision of the outputs they reveal to an analyst. We assume that the analyst performs linear regression on this dataset, and individuals benefit from the outcome of this estimation. We model this scenario as a game where individuals minimize a cost comprising two components: (a) an (agent-specific) disclosure cost for providing high-precision data; and (b) a (global) estimation cost representing the inaccuracy in the linear model estimate. In this game, the linear model estimate is a public good that benefits all individuals. We establish that this game has a unique non-trivial Nash equilibrium. We study the efficiency of this equilibrium and we prove tight bounds on the price of stability for a large class of disclosure and estimation costs. Finally, we study the estimator accuracy achieved at equilibrium. We show that, in general, Aitken's theorem does not hold under strategic data sources, though it does hold if individuals have identical disclosure costs (up to a multiplicative factor). When individuals have non-identical costs, we derive a bound on the improvement of the equilibrium estimation cost that can be achieved by deviating from GLS, under mild assumptions on the disclosure cost functions.