AI 中文总结
针对源数据仅观测部分目标协变量的异构特征空间问题，提出基于投影插补和重要性加权的迁移学习方法，并建立收敛速率保证。
AI 中文摘要
迁移学习通过利用相关的源数据来提升目标任务的表现。大多数方法假设特征空间共享，然而在许多应用中，每个源仅观测到目标协变量的一个子集。由于块缺失，经典的插补方法在此失效，且标准插补矩阵并非针对目标参数估计进行优化。我们研究低维和高维线性回归，并提出异构重要性加权（HIW）方法。该方法通过基于投影的插补对齐特征空间，并通过样本选择的重要性加权传递信息。该框架可容纳多样的投影矩阵以构建面向目标的插补。我们开发了一种基于分类的程序，利用伪响应估计权重的条件误差密度。我们建立了估计量的逐元素和全局收敛速率，数值实验和真实数据研究证明了其有效性。
英文摘要
Transfer learning improves target-task performance by leveraging related source data. Most methods assume shared feature spaces, yet in many applications, each source observes only a subset of target covariates. Classical imputation fails here due to block missingness, and standard imputation matrices are not optimized for target parameter estimation. We study low- and high-dimensional linear regression and propose Heterogeneous Importance Weighting (HIW). Our method aligns feature spaces via projection-based imputation and transfers information through sample-selected importance weighting. This framework accommodates diverse projection matrices to construct target-oriented imputation. We develop a classification-based procedure with pseudo-responses to estimate conditional error densities for the weights. We establish entry-wise and global convergence rates for the estimator, with numerical and real-data studies demonstrating its effectiveness.
Comments24 pages, 3 figures
