Representation Transfer Learning for Semiparametric Regression

TL;DR

This paper introduces a transfer learning approach for semiparametric regression that leverages shared data representations from source domains to improve inference on target domain parameters, accommodating nonlinear confounder effects.

Contribution

It develops a novel transfer learning method using data representations for semiparametric regression, with theoretical guarantees and practical validation.

Findings

Estimator is consistent and asymptotically normal.

Method improves inference accuracy in target domain.

Simulation and real data demonstrate effectiveness.

Abstract

We propose a transfer learning method that utilizes data representations in a semiparametric regression model. Our aim is to perform statistical inference on the parameter of primary interest in the target model while accounting for potential nonlinear effects of confounding variables. We leverage knowledge from source domains, assuming that the sample size of the source data is substantially larger than that of the target data. This knowledge transfer is carried out by the sharing of data representations, predicated on the idea that there exists a set of latent representations transferable from the source to the target domain. We address model heterogeneity between the source and target domains by incorporating domain-specific parameters in their respective models. We establish sufficient conditions for the identifiability of the models and demonstrate that the estimator for the primary parameter in the target model is both consistent and asymptotically normal. These results lay the theoretical groundwork for making statistical inferences about the main effects. Our simulation studies highlight the benefits of our method, and we further illustrate its practical applications using real-world data.