Shoiuld Humans Lie to Machines: The Incentive Compatibility of Lasso and General Weighted Lasso

TL;DR

This paper investigates the incentive compatibility of Lasso and weighted Lasso estimators in machine learning, providing conditions under which users have no incentive to misreport data, supported by theoretical analysis and simulations.

Contribution

It offers new theoretical conditions ensuring incentive compatibility for Lasso and weighted Lasso, extending previous results and providing practical guidelines.

Findings

Incentive compatibility depends on the tuning parameter threshold.

The paper extends results to Conservative Lasso with new moment bounds.

Simulations demonstrate practical implementation of the conditions.

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 large samples. We extend our results to the Conservative Lasso estimator and provide new moment bounds for this generalized weighted version of Lasso. Our results show that incentive compatibility is achieved if the tuning parameter is kept above some threshold. We present simulations that illustrate how this can be done in practice.