Unsupervised Supervised Learning II: Margin-Based Classification Without Labels

Abstract

Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing a margin-based risk function. Traditionally, these risk functions are computed based on a labeled data set. We develop a novel technique for estimating such risks using only unlabeled data and the marginal label distribution. We prove that the proposed risk estimator is consistent on high-dimensional data sets 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 with no labeled data whatsoever.