Robust Transfer Learning for High-Dimensional GLM Using γ $$ \gamma $$ -Divergence With Applications to Cancer Genomics.

Abstract

In the analysis of complex diseases, high-dimensional profiling data is important for assessing risks and detecting biomarkers. With the increasing accessibility of cancer genomic data, the sample sizes remain limited in most studies. Hence, borrowing information from additional data sources is thus desirable to improve estimation and prediction. Transfer learning has been demonstrated to be flexible and effective in boosting modeling performance with a record in biomedical applications. In practice, outliers and even data contamination often occur. However, existing transfer learning methods often lack robustness to outliers and data contamination, issues commonly observed in real-world biomedical data. In this study, we propose a robust transfer learning approach based on the minimum $\gamma$ -divergence under a generalized linear model (GLM) framework for high-dimensional data. Our method incorporates a data-driven source detection scheme that automatically identifies informative sources while mitigating the risk of negative transfer. We establish rigorous theoretical results, including consistency and high-dimensional estimation error bounds, ensuring robustness and reliable performance. A computationally efficient algorithm is developed based on proximal gradient descent to facilitate both the transfer and debiasing steps. Simulation demonstrates the superior and competitive performance of the proposed approach in selection and prediction/classification. We further validate its practical utility by analyzing data on breast cancer and glioblastoma, showcasing the method's effectiveness in real-world high-dimensional settings.