  Consider semi-supervised learning for classification, where both labeled and
unlabeled data are available for training. The goal is to exploit both datasets
to achieve higher prediction accuracy than just using labeled data alone. We
develop a semi-supervised logistic learning method based on exponential tilt
mixture models, by extending a statistical equivalence between logistic
regression and exponential tilt modeling. We study maximum nonparametric
likelihood estimation and derive novel objective functions which are shown to
be Fisher consistent. We also propose regularized estimation and construct
simple and highly interpretable EM algorithms. Finally, we present numerical
results which demonstrate the advantage of the proposed methods compared with
existing methods.
