Transfer learning (TL) has emerged as a powerful tool for improving estimation and prediction performance by leveraging information from related datasets, with the offset TL (O-TL) being a prevailing implementation. In this paper, we adapt the control-variates (CVS) method for TL and develop CVS-based estimators for scalar-on-function regression, one of the most fundamental models in functional data analysis. These estimators rely exclusively on dataset-specific summary statistics, thereby avoiding the pooling of subject-level data and remaining applicable in privacy-restricted or decentralized settings. We establish, for the first time, a theoretical connection between O-TL and CVS-based TL, showing that these two seemingly distinct TL strategies adjust local estimators in fundamentally similar ways. We further derive convergence rates that explicitly account for the unavoidable but typically overlooked smoothing error arising from discretely observed functional predictors, and clarify how similarity among covariance functions across datasets governs the performance of TL. Numerical studies support the theoretical findings and demonstrate that the proposed methods achieve competitive estimation and prediction performance compared with existing alternatives.

翻译：迁移学习（TL）已成为一种通过利用相关数据集信息来提升估计与预测性能的强大工具，其中偏移迁移学习（O-TL）是一种主流的实现方式。本文采用控制变量（CVS）方法进行迁移学习，并针对函数数据分析中最基础的模型之一——标量对函数回归，开发了基于CVS的估计量。这些估计量完全依赖于数据集特定的汇总统计量，从而避免了主体层面数据的汇集，适用于隐私受限或去中心化的场景。我们首次建立了O-TL与基于CVS的TL之间的理论联系，表明这两种表面上不同的TL策略在根本上以相似的方式调整局部估计量。我们进一步推导了收敛速率，其中明确考虑了因函数预测变量离散观测而产生的不可避免但通常被忽略的平滑误差，并阐明了数据集间协方差函数的相似性如何主导迁移学习的性能。数值研究支持了理论发现，并证明所提方法在估计和预测性能上相较于现有替代方案具有竞争力。