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In this work, we present an approach for unsupervised domain adaptation (DA) with the constraint, that the labeled source data are not directly available, and instead only access to a classifier trained on the source data is provided. Our solution, iteratively labels only high confidence sub-regions of the target data distribution, based on the belief of the classifier. Then it iteratively learns new classifiers from the expanding high-confidence dataset. The goal is to apply the proposed approach on DA for the task of sleep apnea detection and achieve personalization based on the needs of the patient. In a series of experiments with both open and closed sleep monitoring datasets, the proposed approach is applied to data from different sensors, for DA between the different datasets. The proposed approach outperforms in all experiments the classifier trained in the source domain, with an improvement of the kappa coefficient that varies from 0.012 to 0.242. Additionally, our solution is applied to digit classification DA between three well established digit datasets, to investigate the generalizability of the approach, and to allow for comparison with related work. Even without direct access to the source data, it achieves good results, and outperforms several well established unsupervised DA methods.