Semi-Unsupervised Learning with Deep Generative Models: Clustering and Classifying using Ultra-Sparse Labels

We introduce $\textit{semi-unsupervised learning}$, an extreme case of semi-supervised learning with ultra-sparse categorisation where some classes have no labels in the training set. That is, in the training data some classes are sparsely labelled and other classes appear only as unlabelled data. Many real-world datasets are conceivably of this type. We demonstrate that effective learning in this regime is only possible when a model is capable of capturing both semi-supervised and unsupervised learning. We develop two deep generative models for classification in this regime that extend previous deep generative models designed for semi-supervised learning. By changing their probabilistic structure to contain a mixture of Gaussians in their continuous latent space, these new models can learn in both unsupervised and semi-unsupervised paradigms. We demonstrate their performance both for semi-unsupervised and unsupervised learning on various standard datasets. We show that our models can learn in an semi-unsupervised manner on Fashion-MNIST. Here we artificially mask out all labels for half of the classes of data and keep $2\%$ of labels for the remaining classes. Our model is able to learn effectively, obtaining a trained classifier with $(77.2\pm1.3)\%$ test set accuracy. We also can train on Fashion-MNIST unsupervised, obtaining $(75.2\pm1.5)\%$ test set accuracy. Additionally, doing the same for MNIST unsupervised we get $(96.3\pm0.9)\%$ test set accuracy, which is state-of-the art for fully probabilistic deep generative models.