【数学与统计及交叉学科前沿论坛------高端学术讲座第147场】

报告题目：Residual Importance Weighted Transfer Learning For High-dimensional Linear Regression

报 告 人：赵俊龙教授 北京师范大学

报告时间：3月14日星期五16:00-17:00

报告地点：阜成路校区教二楼303室

报告摘要：Transfer learning is an emerging paradigm for leveraging multiple source data to improve the statistical inference on a single target data. In this paper, we propose a novel approach named residual importance weighted transfer learning (RIW-TL) for high-dimensional linear models built on LASSO. Compared to existing methods such as Trans-Lasso that selects source data in an allin- all-out manner, RIW-TL includes samples via importance weighting. To determine the weights,remarkably RIW-TL only requires one-dimensional density estimation by weighting residuals, thus overcoming the curse of dimensionality of having to estimate high-dimensional densities in naïve importance weighting. We show that the oracle RIW-TL provides faster rate than its competitors and develop a cross- tting procedure to estimate this oracle. We discuss variants of RIW-TL by adopting dierent 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 simulations and a real data analysis con rm the advantages of RIW-TL.

报告人简介：赵俊龙，北京师范大学统计学院教授。主要从事高维数据分析、稳健统计，统计机器学习等领域相关研究。在统计学各类期刊发表论文五十余篇，部分结果发表在统计学国际顶级期刊JRSSB，AOS、JASA，Biometrika，JBES等。主持多项国家自然科学基金项目，参与国家自然科学基金重点项目。