Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Such methods have been adopted in the context of high-dimensional sparse regression, and some Lasso-based algorithms have been invented: Trans-Lasso and Pretraining Lasso are such examples. These algorithms require the statistician to select hyperparameters that control the extent and type of information transfer from related datasets. However, selection strategies for these hyperparameters, as well as the impact of these choices on the algorithm's performance, have been largely unexplored. To address this, we conduct a thorough, precise study of the algorithm in a high-dimensional setting via an asymptotic analysis using the replica method. Our approach reveals a surprisingly simple behavior of the algorithm: Ignoring one of the two types of information transferred to the fine-tuning stage has little effect on generalization performance, implying that efforts for hyperparameter selection can be significantly reduced. Our theoretical findings are also empirically supported by real-world applications on the IMDb dataset.

本研究解决了高维稀疏回归中超参数选择策略缺乏有效指导的问题，提出了一种基于尖锐渐近分析的方法。研究表明，在精细调整阶段忽略两种信息来源之一对泛化性能影响甚微，从而明显简化了超参数选择的过程。理论发现得到了IMDb数据集的实证支持，展示了方法的实际应用潜力。

基于尖锐渐近分析的$\ell_1$正则回归中的迁移学习：超参数选择策略