Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this limitation, we introduce a novel transfer learning framework for regression models whose outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications. The code is available at https://github.com/h7nian/WaTL

翻译：迁移学习是一种强大的范式，它利用源领域的知识来增强目标领域的学习效果。然而，传统的迁移学习方法通常侧重于欧几里得空间内的标量或多变量数据，这限制了其在复杂数据结构（如概率分布）上的适用性。为解决这一局限性，我们引入了一种新颖的迁移学习框架，用于处理输出为Wasserstein空间中概率分布的回归模型。当可迁移源领域的信息子集已知时，我们提出了一种具有可证明渐近收敛速率的估计器，量化了领域相似性对迁移效率的影响。对于信息子集未知的情况，我们开发了一种数据驱动的迁移学习程序，旨在减轻负迁移。所提出的方法得到了严格的理论分析支持，并通过广泛的模拟和实际应用得到了验证。代码可在 https://github.com/h7nian/WaTL 获取。