A User-Friendly Computational Framework for Robust Structured Regression with the L₂ Criterion

We introduce a user-friendly computational framework for implementing robust versions of a wide variety of structured regression methods with the L2 criterion. In addition to introducing an algorithm for performing L2E regression, our framework enables robust regression with the L2 criterion for additional structural constraints, works without requiring complex tuning procedures on the precision parameter, can be used to identify heterogeneous subpopulations, and can incorporate readily available nonrobust structured regression solvers. We provide convergence guarantees for the framework and demonstrate its flexibility with some examples. Supplementary materials for this article are available online.