A Note on Estimation Error Bound and Grouping Effect of Transfer Elastic Net

TL;DR

This paper introduces a non-asymptotic error bound for the Transfer Elastic Net, a method combining $ ext{l}_1$ and $ ext{l}_2$ penalties for linear regression, and explores its grouping effect in correlated predictors.

Contribution

It provides the first non-asymptotic error bound for Transfer Elastic Net and analyzes conditions for its effective use and grouping effect.

Findings

Derived a non-asymptotic $ ext{l}_2$ error bound

Identified scenarios where Transfer Elastic Net performs well

Demonstrated the grouping effect in highly correlated predictors

Abstract

The Transfer Elastic Net is an estimation method for linear regression models that combines $\ell_1$ and $\ell_2$ norm penalties to facilitate knowledge transfer. In this study, we derive a non-asymptotic $\ell_2$ norm estimation error bound for the estimator and discuss scenarios where the Transfer Elastic Net effectively works. Furthermore, we examine situations where it exhibits the grouping effect, which states that the estimates corresponding to highly correlated predictors have a small difference.