Transfer Learning for Moderate-Dimensional Ridge-Regularized Robust Linear Regression

TL;DR

This paper introduces Trans-RR, a transfer learning method for ridge-regularized robust linear regression in moderate dimensions, demonstrating improved accuracy by leveraging source data.

Contribution

It proposes a novel transfer learning estimator that combines source and target data for robust linear regression without assuming sparsity.

Findings

Leveraging source data can significantly improve estimation accuracy.

Theoretical characterization of asymptotic estimation error is provided.

Simulation and real-data results illustrate both positive and negative transfer effects.

Abstract

This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed to be sparse. We propose Trans-RR, which combines a robust ridge estimator from a source study with a robust ridge correction based on the target study. Under mild assumptions, we characterize the asymptotic estimation error of the proposed estimator and show that leveraging source data can substantially improve estimation accuracy relative to the traditional single-study ridge-regularized robust estimator. Simulation results and a real-data analysis support the theory and illustrate both positive and negative transfer as the discrepancy between the source and target studies varies.