Robust Transfer Learning for High-Dimensional Penalized Linear Regression with t-distributed Error

Abstract

Abstract Background: This paper studies the robust transfer learning for high-dimensional penalized linear regression with t-distributed error (Trans-PtLR), using information from diverse available source datasets to improve the estimation and prediction of the target data, accounting for the problem that normal linear regression is sensitive to outliers or heavy-tailed errors. Method: In transfer learning with known transferable sources, we propose the PtLR model with an unknown degrees-of-freedom of the t distribution to transfer information from heterogeneous sources to the target. Assuming the error term follows a t distribution, the computation of maximum likelihood estimation of model effects and degrees-of-freedom is achieved via a coordinated descent algorithm nested inside the expectation conditional maximization (ECM) algorithm. To avoid negative transfer, a data-driven transferable source detection algorithm is applied to exclude non-informative sources. The performance of the proposed Trans-PtLR is evaluated through extensive simulation studies and an application using Genotype-Tissue Expression (GTEx) data to predict gene expression levels. Result: We compare the performance of Trans-PtLR and transfer learning for penalized normal linear model (Trans-PNLR) under different data patterns. Simulation results indicate that the Trans-PtLR substantially outperforms Trans-PNLR in estimation and variable selection accuracy when outliers and heavy-tail are present in the data. In application, Trans-PtLR can further reduce the average relative prediction error by 42.2%, outperforming Trans-PNLR with an average reduction of 23.7%. Conclusion: The proposed transfer learning for penalized t-linear regression (Trans-PtLR) offers robustness and flexibility to accommodate complex data with outliers and heavytails.