A Generalized Linear Joint Trained Framework for Semi-Supervised Learning 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 attractive properties, originated from a combination of ℓ 1 and ℓ 2 norms, 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 statistical research. Despite this interest, few researchers 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 (s 2 net), which extends the supervised elastic net method, with a general mathematical formulation that covers, but is not limited to, both regression and classification problems. In addition, a flexible and fast implementation for s 2 net is provided. Its advantages are illustrated in different experiments using real and synthetic data sets. They show how s 2 net improves the performance of other techniques that have been proposed for both supervised and semi-supervised learning.