Strategyproof Linear Regression in High Dimensions
This addresses the issue of noise in training data for linear regression by ensuring strategyproofness, which is incremental as it extends known results from two dimensions to high dimensions.
The paper tackles the problem of aligning incentives in linear regression to prevent data manipulation by agents, and discovers a family of group strategyproof mechanisms that work in any number of dimensions, leveraging a connection to the Ham Sandwich Theorem.
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.