The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we study domain generalization as a problem of functional regression. Our concept leads to a new algorithm for learning a linear operator from marginal distributions of inputs to the corresponding conditional distributions of outputs given inputs. Our algorithm allows a source distribution-dependent construction of reproducing kernel Hilbert spaces for prediction, and, satisfies finite sample error bounds for the idealized risk. Numerical implementations and source code are available.

翻译：域泛化问题是指：给定来自不同源分布的数据，学习一个模型，使其能够有效地泛化到仅通过未标注样本观测的新目标分布上。本文从函数回归的角度研究域泛化问题。这一概念引导我们提出一种新算法，该算法能够学习从输入边缘分布到相应给定输入条件下的输出条件分布的线性算子。该算法允许基于源分布构建用于预测的再生核希尔伯特空间，并满足理想风险的有限样本误差界。相关数值实现与源代码均已公开。