Augmented Transfer Regression Learning with Semi-non-parametric Nuisance Models

In contemporary statistical learning, covariate shift correction plays an important role in transfer learning when distribution of the testing data is shifted from the training data. Importance weighting, as a natural and principle strategy to adjust for covariate shift, has been commonly used in the field of transfer learning. However, this strategy is not robust to model misspecification or excessive estimation error. In this paper, we propose an augmented transfer regression learning (ATReL) approach that introduces an imputation model for the targeted response, and uses it to augment the importance weighting equation. With novel semi-non-parametric constructions and calibrated moment estimating equations for the two nuisance models, our ATReL method is less prone to (i) the curse of dimensionality compared to nonparametric approaches, and (ii) model mis-specification than parametric approaches. We show that our ATReL estimator is root-n-consistent when at least one nuisance model is correctly specified, estimation for the parametric part of the nuisance models achieves parametric rate, and the nonparametric components are rate doubly robust. Simulation studies demonstrate that our method is more robust and efficient than existing parametric and fully nonparametric (machine learning) estimators under various configurations. We also examine the utility of our method through a real example about transfer learning of phenotyping algorithm for rheumatoid arthritis across different time windows. Finally, we propose ways to enhance the intrinsic efficiency of our estimator and to incorporate modern machine learning methods with our proposed framework.