A Two-Stage Approach to Multivariate Linear Regression with Sparsely Mismatched Data

Understand

A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units.

• A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled Sensing and ``Regression with Unknown Permutation''.
• In this paper, we study the setup of multiple response variables and a notion of mismatches that generalizes permutations in order to allow for missing matches as well as for one-to-many matches.
• A two-stage method is proposed under the assumption that most pairs are correctly matched.