TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression

TL;DR

This paper introduces TransFusion, a transfer learning method for high-dimensional regression that is robust to covariate shifts, using a novel fused-regularizer and a two-step approach, with theoretical guarantees and distributed extension.

Contribution

The paper proposes a new fused-regularizer-based transfer learning method that handles covariate shifts in high-dimensional regression, with theoretical bounds and a distributed implementation.

Findings

Nonasymptotic estimation error bounds demonstrate robustness.

Method achieves minimax-optimality under certain conditions.

Numerical tests confirm theoretical robustness to covariate shifts.

Abstract

The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this work, we tackle model shifts in the presence of covariate shifts in the high-dimensional regression setting. Specifically, we propose a two-step method with a novel fused-regularizer that effectively leverages samples from source tasks to improve the learning performance on a target task with limited samples. Nonasymptotic bound is provided for the estimation error of the target model, showing the robustness of the proposed method to covariate shifts. We further establish conditions under which the estimator is minimax-optimal. Additionally, we extend the method to a distributed setting, allowing for a pretraining-finetuning strategy, requiring just one round of communication while retaining the estimation rate of the centralized version. Numerical tests validate our theory, highlighting the method's robustness to covariate shifts.