Dissertation Colloquium: Regularized Domain Adaptation in Reproducing Kernel Hilbert Spaces.
Abstract: In machine learning, the domain adaptation problem arises when a core assumption of the statistical learning theory is violated. The above assumption supposes that previously seen and future inputs/outputs of the systems under consideration are governed by the same probability law. Since, in reality, it is not often the case, the domain adaptation problem becomes practically important. In the present study we analyse the use of the general regularization scheme in the scenario of unsupervised domain adaptation under the so-called 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 learning algorithms and discuss how to resolve the issue with the tuning of their parameters. The theoretical results are supported by extensive numerical experiments with various datasets.