Robust Semi-Supervised Learning when Labels are Missing at Random

Semi-supervised learning methods are motivated by the relative paucity of labeled data and aim to utilize large sources of unlabeled data to improve predictive tasks. It has been noted, however, such improvements are not guaranteed in general in some cases the unlabeled data impairs the performance. A fundamental source of error comes from restrictive assumptions about the unlabeled features. In this paper, we develop a semi-supervised learning approach that relaxes such assumptions and is robust with respect to labels missing at random. The approach ensures that uncertainty about the classes is propagated to the unlabeled features in a robust manner. It is applicable using any generative model with associated learning algorithm. We illustrate the approach using both standard synthetic data examples and the MNIST data with unlabeled adversarial examples.