Minimax optimal transfer learning for high-dimensional additive regression

Many human tasks benefit from prior experience when that experience is related to the task at hand. This phenomenon, whereby knowledge from previous tasks is transferred to new ones, has motivated the machine learning technique known as transfer learning. From a statistical perspective, consider the problem of analyzing a regression relationship when the available data are limited. Transfer learning (Torrey and Shavlik (2010)), one of the most widely used techniques in machine learning, can provide a solution. In this framework, one typically leverages related estimates obtained from large but non-identically distributed auxiliary samples, and then refines these estimates to obtain improved estimators from the smaller target sample. Transfer learning has been shown to be effective in a wide range of real-world applications, including computer vision (Kolesnikov et al. (2020); Bu et al. (2021)), natural language processing (Lee et al. (2020); Yuan et al. (2020)), and bioinformatics (Vorontsov et al. (2024); Gao and Cui (2020)), among others. Recently, the theoretical properties of transfer-learned estimators have been extensively investigated across a range of statistical problems.