Residual Importance Weighted Transfer Learning for High-dimensional Linear Regression
提出残差重要性加权迁移学习（RIW-TL）方法，通过重要性加权更有效地利用多个源数据改进高维线性模型的目标推断，克服了传统方法样本选择局限和高维密度估计难题。
Transfer learning is an emerging paradigm for leveraging multiple sources to improve the statistical inference on a single target. In this paper, we propose a novel approach named residual importance weighted transfer learning (RIW-TL) for high-dimensional linear models built on penalized likelihood. Compared to existing methods such as Trans-Lasso that selects sources in an (approximately) all-in-or-all-out manner, RIW-TL includes samples via importance weighting and thus may permit more effective sample use. To determine the weights, remarkably RIW-TL only requires the knowledge of one-dimensional densities dependent on residuals, thus overcoming the curse of dimensionality of having to estimate high-dimensional densities in naive importance weighting. We show that the oracle RIW-TL provides faster rate than its competitors and develop a cross-fitting procedure to estimate this oracle. We discuss variants of RIW-TL by adopting different choices for residual weighting. The theoretical properties of RIW-TL and its variants are established and compared with those of LASSO and Trans-Lasso. Extensive simulation and a real data analysis confirm its advantages.