A Robust Transfer Learning Approach for High-dimensional Linear Regression to Support Integration of Multi-source Gene Expression Data

Transfer learning aims to integrate useful information from multi-source datasets to improve the learning performance of target data. This can be effectively applied in genomics when we learn the gene associations in a target tissue, and data from other tissues can be integrated. However, heavy-tail distribution and outliers are common in genomics data, which poses challenges to the effectiveness of current transfer learning approaches. In this paper, we study the transfer learning problem under high-dimensional linear models with t-distributed error (Trans-PtLR), which aims to improve the estimation and prediction of target data by borrowing information from useful source data and offering robustness to accommodate complex data with heavy tails and outliers. In the oracle case with known transferable source datasets, a transfer learning algorithm based on penalized maximum likelihood and expectation-maximization algorithm is established. To avoid including non-informative sources, we propose to select the transferable sources based on cross-validation. Extensive simulation experiments as well as an application demonstrate that Trans-PtLR demonstrates robustness and better performance of estimation and prediction when heavy-tail and outliers exist compared to transfer learning for linear regression model with normal error distribution. Data integration, Variable selection, T distribution, Expectation maximization algorithm, Genotype-Tissue Expression, Cross validation.