The homogeneity, or more generally, the similarity between source domains and a target domain seems to be essential to a positive transfer learning. In practice, however, the similarity condition is difficult to check and is often violated. In this paper, instead of the popularly used similarity condition, a seeming similarity is introduced, which is defined by a non-orthogonality together with a smoothness. Such a condition is naturally satisfied under common situations and even implies the dissimilarity in some sense. Based on the seeming similarity together with an $L_2$-adjustment, a source-function weighted-transfer learning estimation (sw-TLE) is constructed. By source-function weighting, an adaptive transfer learning is achieved in the sense that it is applied to similar and dissimilar scenarios with a relatively high estimation efficiency. Particularly, under the case with homogenous source and target models, the sw-TLE even can be competitive with the full data estimator. The hidden relationship between the source-function weighting estimator and the James-Stein estimator is established as well, which reveals the structural reasonability of our methodology. Moreover, the strategy does apply to nonparametric and semiparametric models. The comprehensive simulation studies and real data analysis can illustrate that the new strategy is significantly better than the competitors.

翻译：同质性，或更一般地说，源域与目标域之间的相似性，似乎是实现正迁移学习的关键。然而在实践中，相似性条件难以验证且常常被违反。本文引入"看似相似性"概念取代广泛使用的相似性条件，该条件通过非正交性与光滑性共同定义。这种条件在常见情形下自然成立，甚至在一定程度上隐含了不相似性。基于看似相似性结合$L_2$调整，我们构建了源函数加权迁移学习估计（sw-TLE）。通过源函数加权，实现了自适应迁移学习——既能应用于相似场景，也能应用于非相似场景并保持较高估计效率。特别地，在同质源模型与目标模型情形下，sw-TLE甚至能与全数据估计量相媲美。我们还建立了源函数加权估计量与詹姆斯-斯坦估计量之间的隐含联系，揭示了该方法的结构合理性。此外，该策略同样适用于非参数与半参数模型。全面的仿真研究和真实数据分析表明，新策略显著优于现有方法。