Estimation and Inference for High-Dimensional Generalized Linear Models with Knowledge Transfer

• 成果类型: Article
• 署名作者: Li, Sai; Zhang, Linjun; Cai, T. Tony; Li, Hongzhe
• 署名单位: Renmin University of China; Rutgers University System; Rutgers University New Brunswick; University of Pennsylvania; University of Pennsylvania; University of Pennsylvania
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2184373
• 发表日期: 2024
• 页码: 1274-1285
• 关键词: confidence-intervals; Optimal Rates; Lasso

摘要

Transfer learning provides a powerful tool for incorporating data from related studies into a target study of interest. In epidemiology and medical studies, the classification of a target disease could borrow information across other related diseases and populations. In this work, we consider transfer learning for high-dimensional Generalized Linear Models (GLMs). A novel algorithm, TransHDGLM, that integrates data from the target study and the source studies is proposed. Minimax rate of convergence for estimation is established and the proposed estimator is shown to be rate-optimal. Statistical inference for the target regression coefficients is also studied. Asymptotic normality for a debiased estimator is established, which can be used for constructing coordinate-wise confidence intervals of the regression coefficients. Numerical studies show significant improvement in estimation and inference accuracy over GLMs that only use the target data. The proposed methods are applied to a real data study concerning the classification of colorectal cancer using gut microbiomes, and are shown to enhance the classification accuracy in comparison to methods that only use the target data. for this article are available online.