A User-Friendly Computational Framework for Robust Structured Regression with the L${}_2$ Criterion

Abstract

We introduce a user-friendly computational framework for implementing robust versions of a wide variety of structured regression methods with the L${}_2$ criterion. In addition to introducing an algorithm for performing L${}_2$E regression, our framework enables robust regression with the L${}_2$ 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 non-robust 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.