Duc-Hoan Nguyen

We analyze domain adaptation within the framework of reproducing kernel Hilbert spaces under the covariate shift assumption. In this setting, previously known results concerning the least squares excess risk bounds have mainly been derived for importance-weighted kernel ridge regression and either in terms of the smoothness of the target function or in terms of the capacity of the underlying space. The primary novelty of the current research lies in the analysis of general importance-weighted spectral algorithms in both above terms, which enables a substantial improvement of the excess risk bounds. Furthermore, we delve into the covariate shift adaptation utilizing estimated density ratios and explore its application in the context of imbalanced learning from real clinical data.

We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability estimation. To address the above problem, we employ the general regularization scheme in reproducing kernel Hilbert spaces. The convergence rate of the corresponding regularized algorithm is established by taking into account both the smoothness of the derivative and the capacity of the space in which it is estimated. This is done in terms of general source conditions and the regularized Christoffel functions. We also find that the reconstruction of Radon-Nikodym derivatives at any particular point can be done with high order of accuracy. Our theoretical results are illustrated by numerical simulations.

We study the problem of choosing algorithm hyper-parameters in unsupervised domain adaptation, i.e., with labeled data in a source domain and unlabeled data in a target domain, drawn from a different input distribution. We follow the strategy to compute several models using different hyper-parameters, and, to subsequently compute a linear aggregation of the models. While several heuristics exist that follow this strategy, methods are still missing that rely on thorough theories for bounding the target error. In this turn, we propose a method that extends weighted least squares to vector-valued functions, e.g., deep neural networks. We show that the target error of the proposed algorithm is asymptotically not worse than twice the error of the unknown optimal aggregation. We also perform a large scale empirical comparative study on several datasets, including text, images, electroencephalogram, body sensor signals and signals from mobile phones. Our method outperforms deep embedded validation (DEV) and importance weighted validation (IWV) on all datasets, setting a new state-of-the-art performance for solving parameter choice issues in unsupervised domain adaptation with theoretical error guarantees. We further study several competitive heuristics, all outperforming IWV and DEV on at least five datasets. However, our method outperforms each heuristic on at least five of seven datasets.

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.