Semi-supervised oblique predictive clustering trees.

Semi-supervised learning combines supervised and unsupervised learning approaches to learn predictive models from both labeled and unlabeled data. It is most appropriate for problems where labeled examples are difficult to obtain but unlabeled examples are readily available (e.g., drug repurposing). Semi-supervised predictive clustering trees (SSL-PCTs) are a prominent method for semi-supervised learning that achieves good performance on various predictive modeling tasks, including structured output prediction tasks. The main issue, however, is that the learning time scales quadratically with the number of features. In contrast to axis-parallel trees, which only use individual features to split the data, oblique predictive clustering trees (SPYCTs) use linear combinations of features. This makes the splits more flexible and expressive and often leads to better predictive performance. With a carefully designed criterion function, we can use efficient optimization techniques to learn oblique splits. In this paper, we propose semi-supervised oblique predictive clustering trees (SSL-SPYCTs). We adjust the split learning to take unlabeled examples into account while remaining efficient. The main advantage over SSL-PCTs is that the proposed method scales linearly with the number of features. The experimental evaluation confirms the theoretical computational advantage and shows that SSL-SPYCTs often outperform SSL-PCTs and supervised PCTs both in single-tree setting and ensemble settings. We also show that SSL-SPYCTs are better at producing meaningful feature importance scores than supervised SPYCTs when the amount of labeled data is limited.