Domain adaptation aims to use training data from one or multiple source
domains to learn a hypothesis that can be generalized to a different, but
related, target domain. As such, having a reliable measure for evaluating the
discrepancy of both marginal and conditional distributions is crucial. We
introduce Cauchy-Schwarz (CS) divergence to the problem of unsupervised domain
adaptation (UDA). The CS divergence offers a theoretically tighter
generalization error bound than the popular Kullback-Leibler divergence. This
holds for the general case of supervised learning, including multi-class
classification and regression. Furthermore, we illustrate that the CS
divergence enables a simple estimator on the discrepancy of both marginal and
conditional distributions between source and target domains in the
representation space, without requiring any distributional assumptions. We
provide multiple examples to illustrate how the CS divergence can be
conveniently used in both distance metric- or adversarial training-based UDA
frameworks, resulting in compelling performance.

无监督领域适应问题中，为了准确评估边际和条件分布的差异，我们引入了柯西 - 斯瓦兹散度，该散度相比于常用的库尔巴克 - 莱布勒散度提供了更严密的理论广义误差界限，并能方便地用于源领域和目标领域在表示空间中的边际和条件分布差异的估计，而无需任何分布假设。多个示例验证了柯西 - 斯瓦兹散度在基于距离度量或对抗训练的无监督领域适应框架中的出色性能。