A generalized linear joint trained framework for semi-supervised leaning of sparse features

The elastic-net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its nice properties originate from a combination of $\ell_1$ and $\ell_2$ norms, which endow this method with the ability to select variables taking into account the correlations between them. In the last few years, semi-supervised approaches, that use both labeled and unlabeled data, have become an important component in the statistical research. Despite this interest, however, few researches have investigated semi-supervised elastic-net extensions. This paper introduces a novel solution for semi-supervised learning of sparse features in the context of generalized linear model estimation: the generalized semi-supervised elastic-net (s2net), which extends the supervised elastic-net method, with a general mathematical formulation that covers, but is not limited to, both regression and classification problems. We develop a flexible and fast implementation for s2net in R, and its advantages are illustrated using both real and synthetic data sets.