Should Humans Lie to Machines? The Incentive Compatibility of Lasso and GLM Structured Sparsity Estimators

Abstract

We consider situations where a user feeds her attributes to a machine learning method that tries to predict her best option based on a random sample of other users. The predictor is incentive-compatible if the user has no incentive to misreport her covariates. Focusing on the popular Lasso estimation technique, we borrow tools from high-dimensional statistics to characterize sufficient conditions that ensure that Lasso is incentive compatible in the asymptotic case. We extend our results to a new nonlinear machine learning technique, Generalized Linear Model Structured Sparsity estimators. Our results show that incentive compatibility is achieved if the tuning parameter is kept above some threshold in the case of asymptotics.

Keywords:

• Machine learning
• Moment oracle inequality
• Overfit

Supplementary Materials

Supplementary Materials include proofs and simulations.

Acknowledgments

We thank coeditor Ivan Canay and an associate editor and two referees for valuable comments that substantially changed the article. We thank Anders Kock, José Luis Montiel Olea, Ran Spiegler and seminar participants at Simon Fraser University for their valuable comments. We are grateful for the hospitality of the Economics Department at Columbia University, where this research is initiated when both authors were visitors in 2018–2019.

Disclosure Statement

The authors report that there are no competing interests to declare.

Additional information

Funding

Eliaz gratefully acknowledges financial support from ISF grant 470/19.