We analyze the use of the so-called general regularization scheme in the scenario of unsupervised domain adaptation under the covariate shift assumption. Learning algorithms arising from the above scheme are generalizations of importance weighted regularized least squares method, which up to now is among the most used approaches in the covariate shift setting. We explore a link between the considered domain adaptation scenario and estimation of Radon-Nikodym derivatives in reproducing kernel Hilbert spaces, where the general regularization scheme can also be employed and is a generalization of the kernelized unconstrained least-squares importance fitting. We estimate the convergence rates of the corresponding regularized learning algorithms and discuss how to resolve the issue with the tuning of their regularization parameters. The theoretical results are illustrated by numerical examples, one of which is based on real data collected for automatic stenosis detection in cervical arteries.

我们分析了所谓的通用正则化方案在协变量移位假设下的无监督域适应场景中的使用。由上述方案产生的学习算法是重要性加权正则化最小二乘法的推广，这是迄今为止协变量移位设置中最常用的方法之一。我们探索了所考虑的域适应场景与再现核 Hilbert 空间中 Radon-Nikodym 导数的估计之间的联系，其中也可以采用一般正则化方案，并且是核化无约束最小二乘重要性拟合的推广。我们估计相应正则化学习算法的收敛速度，并讨论如何通过调整正则化参数来解决问题。