The Asymptotics of Semi-Supervised Learning in Discriminative Probabilistic Models

Semi-supervised learning aims at taking advantage of unlabeled data to improve the efficiency of supervised learning procedures. For discriminative models however, this is a challenging task. In this contribution, we introduce an original methodology for using unlabeled data through the design of a simple semi-supervised objective function. We prove that the corresponding semi-supervised estimator is asymptotically optimal. The practical consequences of this result are discussed for the case of the logistic regression model.