Profiled Transfer Learning for High Dimensional Linear Model

TL;DR

This paper introduces Profiled Transfer Learning (PTL), a flexible transfer learning method for high-dimensional linear models that leverages an approximate-linear relationship between source and target parameters, supported by theoretical guarantees and practical demonstrations.

Contribution

The paper proposes a novel PTL methodology based on the approximate-linear assumption, offering a more flexible alternative to existing assumptions, with theoretical analysis and empirical validation.

Findings

PTL estimator is minimax optimal under certain conditions.

PTL demonstrates strong finite sample performance in simulations.

Real data application shows encouraging results.

Abstract

We develop here a novel transfer learning methodology called Profiled Transfer Learning (PTL). The method is based on the \textit{approximate-linear} assumption between the source and target parameters. Compared with the commonly assumed \textit{vanishing-difference} assumption and \textit{low-rank} assumption in the literature, the \textit{approximate-linear} assumption is more flexible and less stringent. Specifically, the PTL estimator is constructed by two major steps. Firstly, we regress the response on the transferred feature, leading to the profiled responses. Subsequently, we learn the regression relationship between profiled responses and the covariates on the target data. The final estimator is then assembled based on the \textit{approximate-linear} relationship. To theoretically support the PTL estimator, we derive the non-asymptotic upper bound and minimax lower bound. We find that the PTL estimator is minimax optimal under appropriate regularity conditions. Extensive simulation studies are presented to demonstrate the finite sample performance of the new method. A real data example about sentence prediction is also presented with very encouraging results.