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

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.