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Semi-supervised learning (SSL) is a common approach to learning predictive models using not only labeled examples, but also unlabeled examples. While SSL for the simple tasks of classification and regression has received a lot of attention from the research community, this is not properly investigated for complex prediction tasks with structurally dependent variables. This is the case of multi-label classification and hierarchical multi-label classification tasks, which may require additional information, possibly coming from the underlying distribution in the descriptive space provided by unlabeled examples, to better face the challenging task of predicting simultaneously multiple class labels. In this paper, we investigate this aspect and propose a (hierarchical) multi-label classification method based on semi-supervised learning of predictive clustering trees. We also extend the method towards ensemble learning and propose a method based on the random forest approach. Extensive experimental evaluation conducted on 23 datasets shows significant advantages of the proposed method and its extension with respect to their supervised counterparts. Moreover, the method preserves interpretability and reduces the time complexity of classical tree-based models.