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：域泛化问题旨在从不同源分布的数据中学习一个模型，使其能够泛化到仅通过无标签样本观察到的新目标分布上。本文将域泛化问题视为一种泛函回归问题。基于这一概念，我们提出了一种新算法，用于学习从输入边缘分布到相应输入条件下输出条件分布的线性算子。该算法允许根据源分布构建用于预测的再生核希尔伯特空间，并且满足理想风险的有限样本误差界。数值实现与源代码均已公开。