将迁移学习拓展到概率分布空间，解决复杂数据结构的跨域知识迁移问题。
Wasserstein Transfer Learning
- 在Wasserstein空间中构建回归模型的迁移学习框架
- 已知可转移源域时，理论证明估计器具有渐近收敛性
- 未知可转移源域时，自动筛选有效源域，避免负迁移
迁移学习是一种利用源域知识提升目标域学习效率的强大范式。然而，传统方法多聚焦于欧几里得空间中的标量或多元数据，难以处理概率分布等复杂数据结构。为此，本文提出一种针对输出为概率分布的回归模型的新型迁移学习框架，其定义在Wasserstein空间中。当已知可转移源域的子集时，我们设计了一个具有可证明渐近收敛率的估计器，量化了域相似性对迁移效率的影响；当该子集未知时，提出一种数据驱动的迁移学习方法以缓解负迁移。所提方法具备严格的理论分析支持，并通过大量模拟实验和真实场景应用验证。代码已公开于 https://github.com/h7nian/WaTL。
原文摘要 · Abstract (English)
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
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