Unsupervised Supervised Learning II: Margin-Based Classification without Labels

Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing margin-based risk functions. Traditionally, these risk functions are computed based on a labeled dataset. We develop a novel technique for estimating such risks using only unlabeled data and knowledge of $p(y)$. We prove that the proposed risk estimator is consistent on high-dimensional datasets and demonstrate it on synthetic and real-world data. In particular, we show how the estimate is used for evaluating classifiers in transfer learning, and for training classifiers using exclusively unlabeled data.