We study few-shot supervised domain adaptation (DA) for regression problems, where only a few labeled target domain data and many labeled source domain data are available. Many of the current DA methods base their transfer assumptions on either parametrized distribution shift or apparent distribution similarities, e.g., identical conditionals or small distributional discrepancies. However, these assumptions may preclude the possibility of adaptation from intricately shifted and apparently very different distributions. To overcome this problem, we propose mechanism transfer, a meta-distributional scenario in which a data generating mechanism is invariant among domains. This transfer assumption can accommodate nonparametric shifts resulting in apparently different distributions while providing a solid statistical basis for DA. We take the structural equations in causal modeling as an example and propose a novel DA method, which is shown to be useful both theoretically and experimentally. Our method can be seen as the first attempt to fully leverage the structural causal models for DA.

翻译：我们研究过少数受监督的回归问题领域适应(DA),因为目前只有少数标注的目标领域数据和许多标签源领域数据。目前的DA方法有许多将其转移假设建立在平衡分布变化或明显的分布相似性的基础上,例如相同的条件差异或小分布差异。然而,这些假设可能排除适应变化复杂和明显非常不同的分布的可能性。为解决这一问题,我们建议了机制转移,即元分布假设,即数据生成机制在域间变化不定。这种转移假设可以容纳导致明显不同分布的非参数变化,同时为DA提供坚实的统计基础。我们以因果建模的结构方程式为例,提出新的DA方法,这在理论上和实验上都证明是有用的。我们的方法可以被看作是为DA充分利用结构性因果模型的首次尝试。