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Learning from positive and unlabeled data, or PU learning, is the setting in which a binary classifier can only train from positive and unlabeled instances, the latter containing both positive as well as negative instances. Many PU applications, e.g., fraud detection, are also characterized by class imbalance, which creates a challenging setting. Not only are fewer minority class examples compared to the case where all labels are known, there is also only a small fraction of unlabeled observations that would actually be positive. Despite the relevance of the topic, only a few studies have considered a class imbalance setting in PU learning. In this paper, we propose a novel technique that can directly handle imbalanced PU data, named the PU Hellinger Decision Tree (PU-HDT). Our technique exploits the class prior to estimate the counts of positives and negatives in every node in the tree. Moreover, the Hellinger distance is used instead of more conventional splitting criteria because it has been shown to be class-imbalance insensitive. This simple yet effective adaptation allows PU-HDT to perform well in highly imbalanced PU data sets. We also introduce PU Stratified Hellinger Random Forest (PU-SHRF), which uses PU-HDT as its base learner and integrates a stratified bootstrap sampling. Our empirical analysis shows that PU-SHRF substantially outperforms state-of-the-art PU learning methods for imbalanced data sets in most experimental settings.

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This study estimates the impact that the program "Salas para la Paz" (Rooms for Peace), implemented by "Promoción de Paz, A.B.P." (Peace Promotion, private association for beneficence), has on different aspects of human development, in individuals with addiction, in Monterrey, México. By testing mean differences and using propensity score matching, group comparisons are made, based on the time the subjects have been in the program. The study is based on information obtained from interviews conducted on the participants, and their families. Results based on the answers of the first group, reveal that the program has little or no effect whatsoever. On the other hand, the answers of the second group lead to mixed results, which tend to confirm that direct participant human development increases starting from the second month of treatment.