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

TL;DR

This paper presents a user-friendly computational framework for robust structured regression using the L2 criterion, enabling flexible, efficient, and robust modeling with theoretical guarantees.

Contribution

It introduces an algorithm for L2E regression, allowing robust structured regression with minimal tuning and broad applicability, including subpopulation identification.

Findings

Framework works without complex tuning procedures

Provides convergence guarantees for the algorithms

Demonstrates flexibility through various examples

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.