In this paper, we propose to estimate model parameters and identify informative source datasets simultaneously for high-dimensional transfer learning problems with the aid of a non-convex penalty, in contrast to the separate useful dataset selection and transfer learning procedures in the existing literature. To numerically solve the non-convex problem with respect to two specific statistical models, namely the sparse linear regression and the generalized low-rank trace regression models, we adopt the difference of convex (DC) programming with the alternating direction method of multipliers (ADMM) procedures. We theoretically justify the proposed algorithm from both statistical and computational perspectives. Extensive numerical results are reported alongside to validate the theoretical assertions. An \texttt{R} package \texttt{MHDTL} is developed to implement the proposed methods.

翻译：本文针对高维迁移学习问题，提出一种借助非凸惩罚同时估计模型参数与识别信息源数据集的方法，区别于现有文献中将有用数据集选择与迁移学习分离的处理流程。针对稀疏线性回归和广义低秩迹回归两种特定统计模型，我们采用凸差规划结合交替方向乘子法来数值求解该非凸问题。我们从统计计算双重视角对提出算法进行了理论论证，并通过大量数值实验验证理论结论。开发了R软件包MHDTL以实现所提方法。