PhD Defense - Duc Hoan Nguyen: Regularization in Reproducing Kernel Hilbert space for Covariate Shift Domain Adaptation
Duc Hoan Nguyen, RICAM
Regularization in Reproducing Kernel Hilbert space for Covariate Shift Domain Adaptation
Tuesday, November 28, 2023, 15:00
RICAM, SP2 416-1
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 tting. 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.