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:鉴于来自不同来源分布的数据,域的概括问题在于从不同来源分布中学习一种模型,这种模型可望对新的目标分布进行广泛概括,而新的目标分布只能通过无标签的样本来观察。在本文中,我们研究域的概括是一个功能回归问题。我们的概念导致一种新的算法,从投入的边际分布到相应的输入输出的有条件分布中学习线性操作员。我们的算法允许根据源分布来构建一种源分布结构,为预测再生产内核Hilbert空间,并满足理想化风险的有限抽样误差。有数字执行和源代码。